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AER210 VECTOR CALCULUS and FLUID MECHA�ICS

Fluid Mechanics Quiz 1

12 November 2009 9:15 am – 10:15 am

Closed Book, no aid sheets

Non-programmable calculators allowed

Instructor: Alis Ekmekci

Family Name: __________________________________________

Given Name: __________________________________________

Student #: __________________________________________

TA Name/Tutorial #: ____________________________________

FOR MARKER USE ONLY

Question Marks Earned

1 16

2 10

3 6

4 10

5 12

TOTAL 54 /50

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1) a) The reservoir shown in the figure contains two immiscible liquids of specific weights γA

and γB, respectively, one above the other. γA > γB. Which graph depicts the correct

distribution of the gage pressure along a vertical line through the liquids? (3 points)

b) What is the pressure at the center of pipe B? (4 points)

c) A clown is riding in an elevator, holding a large helium

The cable to the elevator snaps, allowing the elevator to fall freely. Due to her surprise, the

clown lets go of the balloon string at exactly the instant the elevator cable breaks. According to

the clown, what happens to the balloon? Explain

d) Water is held back by the radial gate shown below. Does the resultant of the pressure forces

acting on the gate pass above the pin, through the pin, or below the pin? (

e) Consider a large cubic ice block floating in seawater. The density of ice is 920 kg/m

density of seawater is 1025 kg/m

surface of the water, determine the height of the ice block below the surface.

A clown is riding in an elevator, holding a large helium-filled balloon on the end

The cable to the elevator snaps, allowing the elevator to fall freely. Due to her surprise, the

clown lets go of the balloon string at exactly the instant the elevator cable breaks. According to

e balloon? Explain. (4 points)

d) Water is held back by the radial gate shown below. Does the resultant of the pressure forces

acting on the gate pass above the pin, through the pin, or below the pin? (2 points)

large cubic ice block floating in seawater. The density of ice is 920 kg/m

density of seawater is 1025 kg/m3. If a 10-cm-high portion of the ice block extends above the

surface of the water, determine the height of the ice block below the surface. (3 points)

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filled balloon on the end of a string.

The cable to the elevator snaps, allowing the elevator to fall freely. Due to her surprise, the

clown lets go of the balloon string at exactly the instant the elevator cable breaks. According to

d) Water is held back by the radial gate shown below. Does the resultant of the pressure forces

points)

large cubic ice block floating in seawater. The density of ice is 920 kg/m3 and the

high portion of the ice block extends above the

points)

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2) The force F on a satellite in the earth’s upper atmosphere depends on the mean path of the

molecules λ (a length), the density ρ, the diameter of the body D, and the molecular speed c.

That is, F = f(λ, ρ, D, c). By dimensional analysis, find the non-dimensional form of this

relationship.

(10 marks)

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3) A block of weight W slides down an inclined plane while lubricated by a thin film of oil with

viscosity μ, as in Figure below. The film contact area is A and its thickness is h. Assuming a

linear velocity distribution in the film, derive an expression for the “terminal” (zero-acceleration)

velocity of the block. (6 points)

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4) A 4-m-high, 5-m-wide rectangular plate blocks the end of a 4-m-deep freshwater channel, as

shown in Figure below. The plate is hinged about a horizontal axis along its upper edge through

a point A and is restrained from opening by a fixed ridge at point B. Determine the force exerted

on the plate by the ridge. (10 points)

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5) An 80-cm-high fish tank of rectangular cross section 2 m × 0.6 m that is initially filled with

water is to be transported on the back of a truck. The truck accelerates from 0 to 90 km/h in 10

seconds. If it is desired that no water spills during acceleration, determine the maximum

allowable initial water height in the tank. If it is wanted to carry as much fluid as possible in the

tank, would you recommend the tank to be aligned with the long or short side parallel to the

direction of motion? (12 points)

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