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Fluid Mechanics and Thermodynamics Weekly Assessed Tutorial Sheets, Student Sheets

The WATS approach to assessment was developed as part of an LTSN Engineering Mini-Project, funded at the University of Hertfordshire which aimed to develop a set of 'student unique' tutorial sheets to actively encourage and improve student participation within a first year first „fluid mechanics and thermodynamics‟ module. Please see the accompanying Mini-Project Report “Improving student success and retention through greater participation and tackling student-unique tutorial sheets” for more information.

The WATS cover core Fluid Mechanics and Thermodynamics topics at first year undergraduate level. 11 tutorial sheets and their worked solutions are provided here for you to utilise in your teaching. The variables within each question can be altered so that each student answers the same question but will need to produce a unique solution.

What follows is a set of STUDENT UNIQUE SHEETS for WATS 8.

For more information on WATS, its use and impact on students please contact Mark Russell, School of Aerospace, Automotive and Design Engineering at University of Hertfordshire.

W|ATS8 Student number 1

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 1

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Q1a). A fluid of relative density 0.91 flows through a pipe of diameter 100 mm at 0.19 m/s. After

passing through a gradual reducer the fluid leaves a 33mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 10° (net force)

(N) [5dp] (2

Mark)

iii) A = 57° (Net force)

(N) [5dp] (2

Mark)

iv) A = 79° (Net force)

(N) [5dp] (2

Mark)

Q2. 9 l/s flows through a contracting elbow which has an angle, ‘A’ of 34° i.e. as shown in

figure Q2. Assume the inlet to the bend is 225 mm diameter and the outlet is 90 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.60 Bar

and the fluids specific gravity is 0.96. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 2

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 2

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Q1a). A fluid of relative density 0.86 flows through a pipe of diameter 85 mm at 0.18 m/s. After

passing through a gradual reducer the fluid leaves a 46mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 21° (net force)

(N) [5dp] (2

Mark)

iii) A = 63° (Net force)

(N) [5dp] (2

Mark)

iv) A = 85° (Net force)

(N) [5dp] (2

Mark)

Q2. 5 l/s flows through a contracting elbow which has an angle, ‘A’ of 58° i.e. as shown in

figure Q2. Assume the inlet to the bend is 280 mm diameter and the outlet is 65 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.90 Bar

and the fluids specific gravity is 0.92. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 3

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 3

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Q1a). A fluid of relative density 0.95 flows through a pipe of diameter 80 mm at 0.30 m/s. After

passing through a gradual reducer the fluid leaves a 29mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 18° (net force)

(N) [5dp] (2

Mark)

iii) A = 44° (Net force)

(N) [5dp] (2

Mark)

iv) A = 85° (Net force)

(N) [5dp] (2

Mark)

Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 70° i.e. as shown in

figure Q2. Assume the inlet to the bend is 165 mm diameter and the outlet is 125 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

1.80 Bar and the fluids specific gravity is 0.85. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 4

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 4

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Q1a). A fluid of relative density 0.95 flows through a pipe of diameter 125 mm at 0.14 m/s. After

passing through a gradual reducer the fluid leaves a 66mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 21° (net force)

(N) [5dp] (2

Mark)

iii) A = 55° (Net force)

(N) [5dp] (2

Mark)

iv) A = 81° (Net force)

(N) [5dp] (2

Mark)

Q2. 6 l/s flows through a contracting elbow which has an angle, ‘A’ of 12° i.e. as shown in

figure Q2. Assume the inlet to the bend is 190 mm diameter and the outlet is 75 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.70 Bar

and the fluids specific gravity is 0.82. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 5

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 5

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Q1a). A fluid of relative density 0.94 flows through a pipe of diameter 90 mm at 0.29 m/s. After

passing through a gradual reducer the fluid leaves a 26mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 27° (net force)

(N) [5dp] (2

Mark)

iii) A = 54° (Net force)

(N) [5dp] (2

Mark)

iv) A = 78° (Net force)

(N) [5dp] (2

Mark)

Q2. 15 l/s flows through a contracting elbow which has an angle, ‘A’ of 39° i.e. as shown in

figure Q2. Assume the inlet to the bend is 270 mm diameter and the outlet is 75 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 1.90 Bar

and the fluids specific gravity is 0.80. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 6

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 6

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Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 110 mm at 0.47 m/s. After

passing through a gradual reducer the fluid leaves a 72mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 20° (net force)

(N) [5dp] (2

Mark)

iii) A = 56° (Net force)

(N) [5dp] (2

Mark)

iv) A = 78° (Net force)

(N) [5dp] (2

Mark)

Q2. 10 l/s flows through a contracting elbow which has an angle, ‘A’ of 37° i.e. as shown in

figure Q2. Assume the inlet to the bend is 275 mm diameter and the outlet is 60 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.70 Bar

and the fluids specific gravity is 0.78. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 7

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 7

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Q1a). A fluid of relative density 0.96 flows through a pipe of diameter 105 mm at 0.41 m/s. After

passing through a gradual reducer the fluid leaves a 44mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 7° (net force)

(N) [5dp] (2

Mark)

iii) A = 46° (Net force)

(N) [5dp] (2

Mark)

iv) A = 68° (Net force)

(N) [5dp] (2

Mark)

Q2. 4 l/s flows through a contracting elbow which has an angle, ‘A’ of 13° i.e. as shown in

figure Q2. Assume the inlet to the bend is 195 mm diameter and the outlet is 75 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.80 Bar

and the fluids specific gravity is 0.86. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 8

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 8

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Q1a). A fluid of relative density 0.99 flows through a pipe of diameter 130 mm at 0.21 m/s. After

passing through a gradual reducer the fluid leaves a 69mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 19° (net force)

(N) [5dp] (2

Mark)

iii) A = 59° (Net force)

(N) [5dp] (2

Mark)

iv) A = 74° (Net force)

(N) [5dp] (2

Mark)

Q2. 9 l/s flows through a contracting elbow which has an angle, ‘A’ of 38° i.e. as shown in

figure Q2. Assume the inlet to the bend is 300 mm diameter and the outlet is 70 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.10 Bar

and the fluids specific gravity is 0.90. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 9

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 9

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Q1a). A fluid of relative density 0.81 flows through a pipe of diameter 135 mm at 0.25 m/s. After

passing through a gradual reducer the fluid leaves a 65mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 25° (net force)

(N) [5dp] (2

Mark)

iii) A = 36° (Net force)

(N) [5dp] (2

Mark)

iv) A = 77° (Net force)

(N) [5dp] (2

Mark)

Q2. 6 l/s flows through a contracting elbow which has an angle, ‘A’ of 38° i.e. as shown in

figure Q2. Assume the inlet to the bend is 220 mm diameter and the outlet is 70 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.70 Bar

and the fluids specific gravity is 0.76. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 10

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 10

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Q1a). A fluid of relative density 0.87 flows through a pipe of diameter 85 mm at 0.08 m/s. After

passing through a gradual reducer the fluid leaves a 36mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 33° (net force)

(N) [5dp] (2

Mark)

iii) A = 48° (Net force)

(N) [5dp] (2

Mark)

iv) A = 80° (Net force)

(N) [5dp] (2

Mark)

Q2. 10 l/s flows through a contracting elbow which has an angle, ‘A’ of 51° i.e. as shown in

figure Q2. Assume the inlet to the bend is 165 mm diameter and the outlet is 140 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

2.00 Bar and the fluids specific gravity is 0.79. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 11

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 11

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Q1a). A fluid of relative density 0.95 flows through a pipe of diameter 85 mm at 0.10 m/s. After

passing through a gradual reducer the fluid leaves a 70mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 4° (net force)

(N) [5dp] (2

Mark)

iii) A = 56° (Net force)

(N) [5dp] (2

Mark)

iv) A = 64° (Net force)

(N) [5dp] (2

Mark)

Q2. 3 l/s flows through a contracting elbow which has an angle, ‘A’ of 38° i.e. as shown in

figure Q2. Assume the inlet to the bend is 290 mm diameter and the outlet is 115 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

1.40 Bar and the fluids specific gravity is 0.88. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 12

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.92 flows through a pipe of diameter 90 mm at 0.34 m/s. After

passing through a gradual reducer the fluid leaves a 58mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 26° (net force)

(N) [5dp] (2

Mark)

iii) A = 44° (Net force)

(N) [5dp] (2

Mark)

iv) A = 71° (Net force)

(N) [5dp] (2

Mark)

Q2. 9 l/s flows through a contracting elbow which has an angle, ‘A’ of 78° i.e. as shown in

figure Q2. Assume the inlet to the bend is 175 mm diameter and the outlet is 105 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

2.00 Bar and the fluids specific gravity is 0.76. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 13

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 13

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Q1a). A fluid of relative density 0.86 flows through a pipe of diameter 140 mm at 0.33 m/s. After

passing through a gradual reducer the fluid leaves a 26mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 11° (net force)

(N) [5dp] (2

Mark)

iii) A = 38° (Net force)

(N) [5dp] (2

Mark)

iv) A = 78° (Net force)

(N) [5dp] (2

Mark)

Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 22° i.e. as shown in

figure Q2. Assume the inlet to the bend is 185 mm diameter and the outlet is 130 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

4.30 Bar and the fluids specific gravity is 0.96. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 14

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 14

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Q1a). A fluid of relative density 0.93 flows through a pipe of diameter 130 mm at 0.39 m/s. After

passing through a gradual reducer the fluid leaves a 35mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 6° (net force)

(N) [5dp] (2

Mark)

iii) A = 52° (Net force)

(N) [5dp] (2

Mark)

iv) A = 80° (Net force)

(N) [5dp] (2

Mark)

Q2. 14 l/s flows through a contracting elbow which has an angle, ‘A’ of 25° i.e. as shown in

figure Q2. Assume the inlet to the bend is 270 mm diameter and the outlet is 50 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.30 Bar

and the fluids specific gravity is 0.83. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 15

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 15

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Q1a). A fluid of relative density 0.86 flows through a pipe of diameter 95 mm at 0.05 m/s. After

passing through a gradual reducer the fluid leaves a 47mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 27° (net force)

(N) [5dp] (2

Mark)

iii) A = 46° (Net force)

(N) [5dp] (2

Mark)

iv) A = 84° (Net force)

(N) [5dp] (2

Mark)

Q2. 3 l/s flows through a contracting elbow which has an angle, ‘A’ of 20° i.e. as shown in

figure Q2. Assume the inlet to the bend is 245 mm diameter and the outlet is 65 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.00 Bar

and the fluids specific gravity is 0.87. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 16

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.96 flows through a pipe of diameter 135 mm at 0.29 m/s. After

passing through a gradual reducer the fluid leaves a 39mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 26° (net force)

(N) [5dp] (2

Mark)

iii) A = 40° (Net force)

(N) [5dp] (2

Mark)

iv) A = 64° (Net force)

(N) [5dp] (2

Mark)

Q2. 11 l/s flows through a contracting elbow which has an angle, ‘A’ of 68° i.e. as shown in

figure Q2. Assume the inlet to the bend is 230 mm diameter and the outlet is 140 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

3.70 Bar and the fluids specific gravity is 0.82. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 17

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 1.00 flows through a pipe of diameter 135 mm at 0.21 m/s. After

passing through a gradual reducer the fluid leaves a 67mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 17° (net force)

(N) [5dp] (2

Mark)

iii) A = 60° (Net force)

(N) [5dp] (2

Mark)

iv) A = 79° (Net force)

(N) [5dp] (2

Mark)

Q2. 15 l/s flows through a contracting elbow which has an angle, ‘A’ of 41° i.e. as shown in

figure Q2. Assume the inlet to the bend is 260 mm diameter and the outlet is 130 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

1.60 Bar and the fluids specific gravity is 0.99. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 18

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.85 flows through a pipe of diameter 110 mm at 0.08 m/s. After

passing through a gradual reducer the fluid leaves a 42mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 23° (net force)

(N) [5dp] (2

Mark)

iii) A = 37° (Net force)

(N) [5dp] (2

Mark)

iv) A = 79° (Net force)

(N) [5dp] (2

Mark)

Q2. 11 l/s flows through a contracting elbow which has an angle, ‘A’ of 56° i.e. as shown in

figure Q2. Assume the inlet to the bend is 205 mm diameter and the outlet is 130 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

3.00 Bar and the fluids specific gravity is 0.91. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 19

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 1.00 flows through a pipe of diameter 135 mm at 0.50 m/s. After

passing through a gradual reducer the fluid leaves a 67mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 8° (net force)

(N) [5dp] (2

Mark)

iii) A = 47° (Net force)

(N) [5dp] (2

Mark)

iv) A = 69° (Net force)

(N) [5dp] (2

Mark)

Q2. 15 l/s flows through a contracting elbow which has an angle, ‘A’ of 50° i.e. as shown in

figure Q2. Assume the inlet to the bend is 160 mm diameter and the outlet is 120 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

2.10 Bar and the fluids specific gravity is 0.83. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 20

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.91 flows through a pipe of diameter 90 mm at 0.14 m/s. After

passing through a gradual reducer the fluid leaves a 54mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 22° (net force)

(N) [5dp] (2

Mark)

iii) A = 42° (Net force)

(N) [5dp] (2

Mark)

iv) A = 66° (Net force)

(N) [5dp] (2

Mark)

Q2. 4 l/s flows through a contracting elbow which has an angle, ‘A’ of 61° i.e. as shown in

figure Q2. Assume the inlet to the bend is 230 mm diameter and the outlet is 80 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.30 Bar

and the fluids specific gravity is 0.93. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 21

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Q1a). A fluid of relative density 1.00 flows through a pipe of diameter 100 mm at 0.24 m/s. After

passing through a gradual reducer the fluid leaves a 71mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 26° (net force)

(N) [5dp] (2

Mark)

iii) A = 52° (Net force)

(N) [5dp] (2

Mark)

iv) A = 84° (Net force)

(N) [5dp] (2

Mark)

Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 28° i.e. as shown in

figure Q2. Assume the inlet to the bend is 290 mm diameter and the outlet is 140 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

2.40 Bar and the fluids specific gravity is 0.77. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 22

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Q1a). A fluid of relative density 0.80 flows through a pipe of diameter 100 mm at 0.23 m/s. After

passing through a gradual reducer the fluid leaves a 26mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 14° (net force)

(N) [5dp] (2

Mark)

iii) A = 55° (Net force)

(N) [5dp] (2

Mark)

iv) A = 79° (Net force)

(N) [5dp] (2

Mark)

Q2. 4 l/s flows through a contracting elbow which has an angle, ‘A’ of 24° i.e. as shown in

figure Q2. Assume the inlet to the bend is 205 mm diameter and the outlet is 75 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.20 Bar

and the fluids specific gravity is 0.78. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 23

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Q1a). A fluid of relative density 0.82 flows through a pipe of diameter 105 mm at 0.47 m/s. After

passing through a gradual reducer the fluid leaves a 54mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 13° (net force)

(N) [5dp] (2

Mark)

iii) A = 50° (Net force)

(N) [5dp] (2

Mark)

iv) A = 68° (Net force)

(N) [5dp] (2

Mark)

Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 52° i.e. as shown in

figure Q2. Assume the inlet to the bend is 235 mm diameter and the outlet is 65 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.70 Bar

and the fluids specific gravity is 0.86. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 24

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Q1a). A fluid of relative density 0.96 flows through a pipe of diameter 80 mm at 0.10 m/s. After

passing through a gradual reducer the fluid leaves a 56mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 26° (net force)

(N) [5dp] (2

Mark)

iii) A = 51° (Net force)

(N) [5dp] (2

Mark)

iv) A = 68° (Net force)

(N) [5dp] (2

Mark)

Q2. 5 l/s flows through a contracting elbow which has an angle, ‘A’ of 57° i.e. as shown in

figure Q2. Assume the inlet to the bend is 270 mm diameter and the outlet is 55 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 1.60 Bar

and the fluids specific gravity is 0.76. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 25

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Q1a). A fluid of relative density 0.81 flows through a pipe of diameter 90 mm at 0.18 m/s. After

passing through a gradual reducer the fluid leaves a 60mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 15° (net force)

(N) [5dp] (2

Mark)

iii) A = 48° (Net force)

(N) [5dp] (2

Mark)

iv) A = 71° (Net force)

(N) [5dp] (2

Mark)

Q2. 8 l/s flows through a contracting elbow which has an angle, ‘A’ of 43° i.e. as shown in

figure Q2. Assume the inlet to the bend is 235 mm diameter and the outlet is 130 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

1.20 Bar and the fluids specific gravity is 0.91. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 26

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Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 145 mm at 0.20 m/s. After

passing through a gradual reducer the fluid leaves a 28mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 14° (net force)

(N) [5dp] (2

Mark)

iii) A = 58° (Net force)

(N) [5dp] (2

Mark)

iv) A = 67° (Net force)

(N) [5dp] (2

Mark)

Q2. 13 l/s flows through a contracting elbow which has an angle, ‘A’ of 55° i.e. as shown in

figure Q2. Assume the inlet to the bend is 250 mm diameter and the outlet is 65 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.80 Bar

and the fluids specific gravity is 0.75. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 27

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Q1a). A fluid of relative density 0.99 flows through a pipe of diameter 140 mm at 0.04 m/s. After

passing through a gradual reducer the fluid leaves a 35mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 24° (net force)

(N) [5dp] (2

Mark)

iii) A = 46° (Net force)

(N) [5dp] (2

Mark)

iv) A = 83° (Net force)

(N) [5dp] (2

Mark)

Q2. 12 l/s flows through a contracting elbow which has an angle, ‘A’ of 22° i.e. as shown in

figure Q2. Assume the inlet to the bend is 220 mm diameter and the outlet is 70 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.00 Bar

and the fluids specific gravity is 0.88. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 28

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Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 135 mm at 0.19 m/s. After

passing through a gradual reducer the fluid leaves a 34mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 9° (net force)

(N) [5dp] (2

Mark)

iii) A = 59° (Net force)

(N) [5dp] (2

Mark)

iv) A = 79° (Net force)

(N) [5dp] (2

Mark)

Q2. 14 l/s flows through a contracting elbow which has an angle, ‘A’ of 34° i.e. as shown in

figure Q2. Assume the inlet to the bend is 250 mm diameter and the outlet is 50 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.00 Bar

and the fluids specific gravity is 0.86. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 29

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.83 flows through a pipe of diameter 95 mm at 0.44 m/s. After

passing through a gradual reducer the fluid leaves a 70mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 31° (net force)

(N) [5dp] (2

Mark)

iii) A = 62° (Net force)

(N) [5dp] (2

Mark)

iv) A = 73° (Net force)

(N) [5dp] (2

Mark)

Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 29° i.e. as shown in

figure Q2. Assume the inlet to the bend is 260 mm diameter and the outlet is 110 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

1.50 Bar and the fluids specific gravity is 0.87. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 30

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.93 flows through a pipe of diameter 125 mm at 0.30 m/s. After

passing through a gradual reducer the fluid leaves a 38mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 26° (net force)

(N) [5dp] (2

Mark)

iii) A = 53° (Net force)

(N) [5dp] (2

Mark)

iv) A = 75° (Net force)

(N) [5dp] (2

Mark)

Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 59° i.e. as shown in

figure Q2. Assume the inlet to the bend is 175 mm diameter and the outlet is 115 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

2.80 Bar and the fluids specific gravity is 0.94. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 31

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 100 mm at 0.04 m/s. After

passing through a gradual reducer the fluid leaves a 62mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 7° (net force)

(N) [5dp] (2

Mark)

iii) A = 46° (Net force)

(N) [5dp] (2

Mark)

iv) A = 86° (Net force)

(N) [5dp] (2

Mark)

Q2. 6 l/s flows through a contracting elbow which has an angle, ‘A’ of 68° i.e. as shown in

figure Q2. Assume the inlet to the bend is 265 mm diameter and the outlet is 70 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.60 Bar

and the fluids specific gravity is 0.92. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 32

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.87 flows through a pipe of diameter 85 mm at 0.08 m/s. After

passing through a gradual reducer the fluid leaves a 33mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 10° (net force)

(N) [5dp] (2

Mark)

iii) A = 34° (Net force)

(N) [5dp] (2

Mark)

iv) A = 67° (Net force)

(N) [5dp] (2

Mark)

Q2. 10 l/s flows through a contracting elbow which has an angle, ‘A’ of 54° i.e. as shown in

figure Q2. Assume the inlet to the bend is 255 mm diameter and the outlet is 95 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 1.30 Bar

and the fluids specific gravity is 0.88. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 33

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.84 flows through a pipe of diameter 95 mm at 0.38 m/s. After

passing through a gradual reducer the fluid leaves a 31mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 26° (net force)

(N) [5dp] (2

Mark)

iii) A = 44° (Net force)

(N) [5dp] (2

Mark)

iv) A = 71° (Net force)

(N) [5dp] (2

Mark)

Q2. 8 l/s flows through a contracting elbow which has an angle, ‘A’ of 59° i.e. as shown in

figure Q2. Assume the inlet to the bend is 210 mm diameter and the outlet is 50 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.40 Bar

and the fluids specific gravity is 0.82. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 34

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.92 flows through a pipe of diameter 115 mm at 0.08 m/s. After

passing through a gradual reducer the fluid leaves a 67mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 6° (net force)

(N) [5dp] (2

Mark)

iii) A = 61° (Net force)

(N) [5dp] (2

Mark)

iv) A = 77° (Net force)

(N) [5dp] (2

Mark)

Q2. 12 l/s flows through a contracting elbow which has an angle, ‘A’ of 49° i.e. as shown in

figure Q2. Assume the inlet to the bend is 185 mm diameter and the outlet is 80 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.50 Bar

and the fluids specific gravity is 0.79. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 35

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.89 flows through a pipe of diameter 95 mm at 0.35 m/s. After

passing through a gradual reducer the fluid leaves a 48mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 23° (net force)

(N) [5dp] (2

Mark)

iii) A = 62° (Net force)

(N) [5dp] (2

Mark)

iv) A = 73° (Net force)

(N) [5dp] (2

Mark)

Q2. 3 l/s flows through a contracting elbow which has an angle, ‘A’ of 25° i.e. as shown in

figure Q2. Assume the inlet to the bend is 220 mm diameter and the outlet is 110 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

4.20 Bar and the fluids specific gravity is 0.80. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 36

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.85 flows through a pipe of diameter 100 mm at 0.26 m/s. After

passing through a gradual reducer the fluid leaves a 36mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 28° (net force)

(N) [5dp] (2

Mark)

iii) A = 53° (Net force)

(N) [5dp] (2

Mark)

iv) A = 84° (Net force)

(N) [5dp] (2

Mark)

Q2. 4 l/s flows through a contracting elbow which has an angle, ‘A’ of 20° i.e. as shown in

figure Q2. Assume the inlet to the bend is 170 mm diameter and the outlet is 90 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.40 Bar

and the fluids specific gravity is 0.87. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 37

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 105 mm at 0.49 m/s. After

passing through a gradual reducer the fluid leaves a 38mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 22° (net force)

(N) [5dp] (2

Mark)

iii) A = 41° (Net force)

(N) [5dp] (2

Mark)

iv) A = 77° (Net force)

(N) [5dp] (2

Mark)

Q2. 15 l/s flows through a contracting elbow which has an angle, ‘A’ of 16° i.e. as shown in

figure Q2. Assume the inlet to the bend is 270 mm diameter and the outlet is 70 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.00 Bar

and the fluids specific gravity is 0.99. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 38

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.98 flows through a pipe of diameter 105 mm at 0.04 m/s. After

passing through a gradual reducer the fluid leaves a 28mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 30° (net force)

(N) [5dp] (2

Mark)

iii) A = 44° (Net force)

(N) [5dp] (2

Mark)

iv) A = 70° (Net force)

(N) [5dp] (2

Mark)

Q2. 3 l/s flows through a contracting elbow which has an angle, ‘A’ of 34° i.e. as shown in

figure Q2. Assume the inlet to the bend is 165 mm diameter and the outlet is 95 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.60 Bar

and the fluids specific gravity is 0.98. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 39

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Q1a). A fluid of relative density 0.93 flows through a pipe of diameter 125 mm at 0.17 m/s. After

passing through a gradual reducer the fluid leaves a 29mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 28° (net force)

(N) [5dp] (2

Mark)

iii) A = 63° (Net force)

(N) [5dp] (2

Mark)

iv) A = 75° (Net force)

(N) [5dp] (2

Mark)

Q2. 3 l/s flows through a contracting elbow which has an angle, ‘A’ of 45° i.e. as shown in

figure Q2. Assume the inlet to the bend is 180 mm diameter and the outlet is 95 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 1.40 Bar

and the fluids specific gravity is 0.97. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 40

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Q1a). A fluid of relative density 0.82 flows through a pipe of diameter 145 mm at 0.34 m/s. After

passing through a gradual reducer the fluid leaves a 38mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 7° (net force)

(N) [5dp] (2

Mark)

iii) A = 52° (Net force)

(N) [5dp] (2

Mark)

iv) A = 72° (Net force)

(N) [5dp] (2

Mark)

Q2. 9 l/s flows through a contracting elbow which has an angle, ‘A’ of 56° i.e. as shown in

figure Q2. Assume the inlet to the bend is 215 mm diameter and the outlet is 130 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

1.70 Bar and the fluids specific gravity is 0.93. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 41

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Q1a). A fluid of relative density 0.94 flows through a pipe of diameter 115 mm at 0.20 m/s. After

passing through a gradual reducer the fluid leaves a 28mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 5° (net force)

(N) [5dp] (2

Mark)

iii) A = 38° (Net force)

(N) [5dp] (2

Mark)

iv) A = 77° (Net force)

(N) [5dp] (2

Mark)

Q2. 7 l/s flows through a contracting elbow which has an angle, ‘A’ of 52° i.e. as shown in

figure Q2. Assume the inlet to the bend is 295 mm diameter and the outlet is 70 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.10 Bar

and the fluids specific gravity is 0.84. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 42

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Q1a). A fluid of relative density 0.97 flows through a pipe of diameter 120 mm at 0.44 m/s. After

passing through a gradual reducer the fluid leaves a 49mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 7° (net force)

(N) [5dp] (2

Mark)

iii) A = 62° (Net force)

(N) [5dp] (2

Mark)

iv) A = 81° (Net force)

(N) [5dp] (2

Mark)

Q2. 10 l/s flows through a contracting elbow which has an angle, ‘A’ of 55° i.e. as shown in

figure Q2. Assume the inlet to the bend is 235 mm diameter and the outlet is 60 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 2.20 Bar

and the fluids specific gravity is 0.84. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 43

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Q1a). A fluid of relative density 0.91 flows through a pipe of diameter 110 mm at 0.21 m/s. After

passing through a gradual reducer the fluid leaves a 47mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 13° (net force)

(N) [5dp] (2

Mark)

iii) A = 51° (Net force)

(N) [5dp] (2

Mark)

iv) A = 80° (Net force)

(N) [5dp] (2

Mark)

Q2. 15 l/s flows through a contracting elbow which has an angle, ‘A’ of 80° i.e. as shown in

figure Q2. Assume the inlet to the bend is 240 mm diameter and the outlet is 125 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

4.90 Bar and the fluids specific gravity is 0.91. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 44

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.89 flows through a pipe of diameter 95 mm at 0.28 m/s. After

passing through a gradual reducer the fluid leaves a 65mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 5° (net force)

(N) [5dp] (2

Mark)

iii) A = 47° (Net force)

(N) [5dp] (2

Mark)

iv) A = 81° (Net force)

(N) [5dp] (2

Mark)

Q2. 13 l/s flows through a contracting elbow which has an angle, ‘A’ of 58° i.e. as shown in

figure Q2. Assume the inlet to the bend is 265 mm diameter and the outlet is 110 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

1.80 Bar and the fluids specific gravity is 0.86. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 45

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

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Q1a). A fluid of relative density 0.90 flows through a pipe of diameter 140 mm at 0.07 m/s. After

passing through a gradual reducer the fluid leaves a 53mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 31° (net force)

(N) [5dp] (2

Mark)

iii) A = 58° (Net force)

(N) [5dp] (2

Mark)

iv) A = 87° (Net force)

(N) [5dp] (2

Mark)

Q2. 15 l/s flows through a contracting elbow which has an angle, ‘A’ of 63° i.e. as shown in

figure Q2. Assume the inlet to the bend is 210 mm diameter and the outlet is 75 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 1.40 Bar

and the fluids specific gravity is 0.90. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 46

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 46

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Q1a). A fluid of relative density 0.89 flows through a pipe of diameter 105 mm at 0.01 m/s. After

passing through a gradual reducer the fluid leaves a 64mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 24° (net force)

(N) [5dp] (2

Mark)

iii) A = 59° (Net force)

(N) [5dp] (2

Mark)

iv) A = 72° (Net force)

(N) [5dp] (2

Mark)

Q2. 12 l/s flows through a contracting elbow which has an angle, ‘A’ of 11° i.e. as shown in

figure Q2. Assume the inlet to the bend is 195 mm diameter and the outlet is 50 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.20 Bar

and the fluids specific gravity is 0.89. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 47

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 47

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Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 95 mm at 0.46 m/s. After

passing through a gradual reducer the fluid leaves a 73mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 15° (net force)

(N) [5dp] (2

Mark)

iii) A = 45° (Net force)

(N) [5dp] (2

Mark)

iv) A = 65° (Net force)

(N) [5dp] (2

Mark)

Q2. 8 l/s flows through a contracting elbow which has an angle, ‘A’ of 47° i.e. as shown in

figure Q2. Assume the inlet to the bend is 290 mm diameter and the outlet is 80 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 3.40 Bar

and the fluids specific gravity is 0.98. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 48

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 48

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Q1a). A fluid of relative density 0.81 flows through a pipe of diameter 130 mm at 0.12 m/s. After

passing through a gradual reducer the fluid leaves a 58mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 23° (net force)

(N) [5dp] (2

Mark)

iii) A = 59° (Net force)

(N) [5dp] (2

Mark)

iv) A = 75° (Net force)

(N) [5dp] (2

Mark)

Q2. 14 l/s flows through a contracting elbow which has an angle, ‘A’ of 76° i.e. as shown in

figure Q2. Assume the inlet to the bend is 225 mm diameter and the outlet is 125 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

2.50 Bar and the fluids specific gravity is 0.96. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 49

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 49

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Q1a). A fluid of relative density 1.00 flows through a pipe of diameter 120 mm at 0.10 m/s. After

passing through a gradual reducer the fluid leaves a 61mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 32° (net force)

(N) [5dp] (2

Mark)

iii) A = 61° (Net force)

(N) [5dp] (2

Mark)

iv) A = 72° (Net force)

(N) [5dp] (2

Mark)

Q2. 9 l/s flows through a contracting elbow which has an angle, ‘A’ of 73° i.e. as shown in

figure Q2. Assume the inlet to the bend is 190 mm diameter and the outlet is 110 mm

diameter and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is

2.10 Bar and the fluids specific gravity is 0.90. Calculate the net force and the direction of the

force acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

W|ATS8 Student number 50

Fluid Mechanics and Thermodynamics. Weekly Assessed Tutorial Sheet 8.

Student Number 50

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Q1a). A fluid of relative density 0.88 flows through a pipe of diameter 115 mm at 0.19 m/s. After

passing through a gradual reducer the fluid leaves a 73mm diameter pipe and discharges onto a

stationary surface. Assuming that the surface slopes at an angle of ‘A’ degrees from the horizontal

plane, as shown below, and that the surface somehow acts as a vane in that the fluid is deflected

along its surface - calculate the forces acting on the surface for the angles shown in the

answer boxes. You may assume that friction effects are negligible.

Figure Q1a. Definition of angle ‘A’ for the inclined surface.

i) A = 90° (X force)

(N) [5dp] (1

Mark)

ii) A = 31° (net force)

(N) [5dp] (2

Mark)

iii) A = 51° (Net force)

(N) [5dp] (2

Mark)

iv) A = 79° (Net force)

(N) [5dp] (2

Mark)

Q2. 8 l/s flows through a contracting elbow which has an angle, ‘A’ of 40° i.e. as shown in

figure Q2. Assume the inlet to the bend is 215 mm diameter and the outlet is 95 mm diameter

and that the pipe lies in the horizontal plane. The static pressure at the pipe inlet is 4.60 Bar

and the fluids specific gravity is 0.79. Calculate the net force and the direction of the force

acting on the bend.

i) Net force (N)

[5dp]

(3 Mark)

ii) Direction of force.

(As measured anti-clockwise from the

top of the horizontal plane. i.e. AS

SHOWN in all above examples. [1dp]

(1 Mark)

Figure Q2. Sketch of bend.

90.0°

A X

Y

45.5°

A

Y

X

52.2°

A

X

Y

_______________________________________________________________________________________________

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© University of Hertfordshire 2009

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