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MA2003 INTRODUCTION TO THERMO-FLUIDS Tutorial 7 Fluid Properties, pressure and manometers

1. Two layers of fluid are dragged along by the motion of an upper plate as shown in Figure 1 with the bottom plate remains stationary. Determine the ratio of shear stress on upper plate to that of lower plate.

Figure 1 Figure 2

2. An inverted 0.1-m-diameter cylinder is partially filled with water and covered by a plate as shown in Figure 2. A force of 20 N is needed to pull the plate away from the cylinder. Determine the air pressure inside the cylinder. Neglect the mass of the plate.

3. Determine the elevation difference, h, between the water levels in the two open

tanks in Figure 3.

Figure 3 Figure 4 4. Determine the density of the unknown liquid occupied the lower half of the tank

(Figure 4). Ans: 1. [1]; 2. [-4.51 kPa]; 3. [0.04 m]; 4. [1930 kg/m3].

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MA2003 INTRODUCTION TO THERMO-FLUIDS Tutorial 8 Manometers, hydrostatic forces

1. Please refer to the figure below. Determine the pressure in pipe B when the pressure

in pipe A is -30mm Hg gauge.(S.G of mercury 13.6 and S.G. of oil 0.7). 2. A gate with the shape as shown in Figure 2 is mounted on a horizontal shaft.

Determine the net moment about the shaft from the hydrostatic forces acting on the gate.

Figure 2 Figure 3 3. Calculate the horizontal and vertical hydrostatic forces acting on the dam shown in

Figure 3 and hence determine the minimum coefficient of friction needed to prevent sliding. Specific weight of concrete is 23.6 kN/m3. Width of the dam is 1 m.

4. A cylindrical tank with its axis horizontal has a diameter of 2.0 m and a length 4.0 m.

The ends of the tank are hemispherical. A vertical, 0.1-m-diameter pipe is connected to the top of the tank. The tank and the pipe are filled with ethyl alcohol (S.G. = 0.79) to a level of 1.5 m above the top of the tank. Determine the horizontal force of alcohol on one of the curved ends.

Ans: 1. [34.3 kPa]; 2. [750 kNm]; 3. [78.4 kN, 62.8 kN, 0.147]; 4. [60.8 kN].

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10 m

300 300

d

Water

Water surface

MA2003 INTRODUCTION TO THERMO-FLUIDS Tutorial 9 Hydrostatic forces, stability, and rigid body motion

1. A conical plug is placed at the bottom of a tank filled with a liquid of specific weight

27 kN/m3 (Figure 1). The air space is pressurized to 50 kPa. Determine the magnitude, dirction and line of action of the force on the curved surface of the cone.

Figure 1 Figure 2 2. A 20-m-long wooden barge has a triangular cross-section as shown in Figure 2. The

barge is submerged to a depth d in the water. Determine the value of d, given that the specific gravity of wood is 0.65. By means of calculations, state whether the barge is stable or not.

3. An open rectangular tank 1m wide and 2 m long contains gasoline to a depth of 1m. If

the height of the tank sides is 1.5 m, what is the maximum horizontal acceleration (along the longitudinal axis) that can develop before the gasoline would begin to spill?

4. The U-tube contains mercury and rotates about the off-center axis a-a. At rest the

depth of mercury in each leg is 150mm. Determine the angular velocity for which the difference in heights between the two legs is 75mm.

Ans: 1. [128 kN]; 2. [2.33 m, stable]; 3. [4.91 m/s2]; 4. [6.04 rad/s]

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MA2003 INTRODUCTION TO THERMO-FLUIDS Tutorial 10 Bernoulli equation

1. Water flows through a pipe reducer as shown. Determine the flow rate, Q, if the

diameter of the smaller pipe D = 0.05m. What would be the flow rate if gasoline is the working fluid?

2. Water of constant depth h flows from a large tank through three pipes of different diameters and inclinations as shown in Fig. 2. Viscous effects are negligible. Determine heights h1, h2 and h3 in terms of h to which the three streams rise.

Figure 2 Figure 3 3. As shown in Fig. 3, determine the height, h, and the pressure inside the horizontal

pipe when the nozzle exit is at the same level as the oil/water interface. Assume ideal flow.

4. Determine the water depth in the upper tank, hA, when the flow reaches a steady condition (i.e. constant water levels in both tanks). Assume frictionless flow.

Ans: 1. [0.0156 m3/s]; 2. [h, h, and 0.5h]; 3. [2.8 m and 35.5 kPa]; 4. [15.4 m]

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MA2003 INTRODUCTION TO THERMO-FLUIDS Tutorial 11 Mass conservation

1. Oil having a specific gravity of 0.9 is pumped as shown to mix with water as shown

in Figure 1. The water flow rate is 2 m3/s. The water and oil mixture has an average specific gravity of 0.95. Calculate the flowrate of oil.

Figure 1 Figure 2 2. A hypodermic syringe is used to apply a vaccine as shown in Figure 2. If the plunger

is moved forward at a steady rate of 20 mm/s and if vaccine leaks past the plunger at 0.1 of the volume flowrate out of the needle opening, calculate the average velocity of the needle exit flow. The inside diameters of the syringe and needle are 20 mm and 0.7 mm.

3. Oil (SG = 0.9) flows downward through a vertical pipe contraction as shown. If the mercury manometer reading, h = 100 mm, determine the volume flowrate for frictionless flow. Is the actual flowrate more or less than the frictionless value? Explain.

Figure 3 Figure 4 4. Estimate the time required to fill with water a cone-shaped container shown in Figure

4 if the filling rate is 76 Liter/min.

Ans: 1. [2.0 m3/s]; 2. [14.8 m/s]; 3. [0.042 m3/s]; 4. [11.6 min]

1.5 m

1.5 m