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Fluid MechanicsChapter :Pressure Distribution in a FluidPart IV

Week 3 Lecture Notes

J. LevisonENGG 2230 Winter

Lecture 6

Thursday, January 23, 2014

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Todays Lecture

Do buoyancy (stability) example

Pressure distribution in rigid body motion

Linear acceleration

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References

F.M. White, Fluid Mechanics, McGraw-Hill, 2011.

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Example 2.6:

A barge is 4.5 m wide and 12 m long andfloats with a draft of 1.2 m. It is piled so high

with gravel that its centre of gravity is 0.6 m

above the waterline. Is it stable?

[draft = vertical distance between the waterline and the

bottom of the hull]

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Fluids in motion

Were almost ready to start studying this

BUT, first we can study one category using

fluid statics concepts

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Whole fluid moves as if it were a rigid (i.e., non-

deforming) body

Individual particles are not deforming (even

though they might be in motion)

Examples:1) fluid traveling on a tank in a train (linear acceleration)

2) cylinder of liquid in rotation at a constant angular speed (rigid-

body rotation)

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Rigid Body Motion

A special case where all particles are incombined translation and rotation with no

relative motion between particles

Sometimes referred to as relative equilibrium With no relative motion, there are no shear

strains or strain rates

Accelerating fluid will t i l t under uniform rigidbody acceleration (like an accelerating glass

of water)

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Accelerating Fluid

9(White: Fig. E2.13)

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Tilt in gof Fluid in Rigid Body Acceleration

10(White: Fig. 2.21)

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Example 2.7:

The tank of liquid in the

figure accelerates to theright with the fluid in rigid

body motion.

a. Compute axin m/s2

b. Why doesnt the solutionin part a depend on the

fluid density?

c. Determine the gauge

pressure at point A if thefluid is glycerin at 20C.

11(White)

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Example 2.8:

The same tank as beforeis now moving with

constant acceleration up a

30 inclined plane.

Assuming rigid body

acceleration compute:

a. The acceleration, a

b. Whether the acceleration

is upwards or downwards

c. Determine the gauge

pressure at point A if the

fluid is mercury at 20C.

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Homework

Assignment #2finish by Sunday(Assignment 1 solutions were posted last Sunday)

Read Sections 3.13.5

Reminder for Week 2 lab groups:

Lab reportsdue by 5 pm one week after you

perform the lab

Submission box #12 in THRN

Review marking scheme in the lab manual

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