4 effect of acceleration on static fluid(1)

8/11/2019 4 Effect of Acceleration on Static Fluid(1)

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ACCELERATION EFFECTON STATIC FLUID


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OBJECTIVES

This chapter is designed to help students achieve the following :- Understanding the effect of the acceleration of the staticfluid.

- Proving that the inclination of the plane surface.

- Shows how the analysis of acceleration effect can assist insolve problems in the field of engineering.


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LEARNING OUTCOMES

At the end of this chapter, students will be able to use

knowledge and skills to :

- Define the effect of acceleration on the static fluid.

- State the basic equations related effects of acceleration on astatic fluid.

- Solve simple problems related effect of acceleration on staticfluid.


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ACCELERATION EFFECT OF STATIC

FLUID

Consider a fluid-filled tank below :


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When subjected to a horizontal directionacceleration, fluid surface will be inclined.

This will affect the pressure on the bottom of the

tank surface Indirectly it will affect the strength of the tank

structure

CONT..


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Consider a small fluid molecules below :

CONT..


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If the molecule is accelerated with the accelerationof the fluid x, ax :

Fx= max

p1A1

p2A2= max(p1p2)A = Vax

(p1p2)yz = xyzax

(p1

p2) = xaxp/x = ax (1)

CONT..


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If the molecule is accelerated with the accelerationof the fluid y, ay :

Fy= may

p1A1

p2A2 - mg = may(p1p2)A = V(ay+g)

(p1p2)xz = xyz(ay+g)

(p1

p2) = y(ay+g)p/y = (ay+g) (2)

CONT..


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If the molecule is accelerated with the accelerationof the fluid z, az :

Fz= maz

p1A1

p2A2= maz(p1p2)A = Vaz

(p1p2)xy = xyzaz

(p1

p2) = zazp/z = az (3)

CONT..


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If the molecules is accelerated to the surface of theinclined fluid to the s axis (the angle will be fromthe x axis to s axis)

p/s = (p/x)(x/s) + (p/y)(y/s)

y

x

s

CONT..


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And is known on the surface of the fluid, thepressure is equal to atmospheric pressure.

So,p/s = 0

0 = (p/x)(x/s) + (p/y)(y/s)

CONT..


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(p/x)(x/s) = - (p/y)(y/s)

(p/x)/(p/y) = -(y/s) )/(x/s)

(y/x) = -(y/s) )/(x/s)

As we know,

(y/x) = tan

So,

tan = -ax/(g +ay)

CONT..


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Conclusion

- Angle of inclination of the water surface when

acceleration can be known with using the above

formula.- When subjected to positive acceleration, angle

inclination of the water surface will be

within the limits of 90 to 180.

CONT..


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EXAMPLE

Example 1

Example 2

Example 3
http://d/KINGSTON%20(G)/BDA1052/LECTURE%20NOTE/TOPIK%204/contoh%201a.dochttp://d/KINGSTON%20(G)/BDA1052/LECTURE%20NOTE/TOPIK%204/contoh%202a.dochttp://d/KINGSTON%20(G)/BDA1052/LECTURE%20NOTE/TOPIK%204/contoh%203a.dochttp://d/KINGSTON%20(G)/BDA1052/LECTURE%20NOTE/TOPIK%204/contoh%203a.dochttp://d/KINGSTON%20(G)/BDA1052/LECTURE%20NOTE/TOPIK%204/contoh%202a.dochttp://d/KINGSTON%20(G)/BDA1052/LECTURE%20NOTE/TOPIK%204/contoh%201a.doc


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THANK YOU

4 effect of acceleration on static fluid(1)

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