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AER210 VECTOR CALCULUS and FLUID MECHA�ICS

Fluid Mechanics Part - Quiz 3

11 November 2010 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 15

2 5

3 10

4 10

5 10

TOTAL 50 /50

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1) a) Air that has a density of ρ = 1.24 kg/m3 flows in a pipe with a diameter of D = 30 cm

at a mass flow rate of m� = 3 kg/s. What are the mean velocity of the flow in this pipe and

the volume flow rate? (3 points)

b) Assume that two layers of fluid is dragged along by the motion of an upper plate as

shown in the Figure below. The top fluid puts a shear stress on the upper plate, and the

lower fluid puts a shear stress on the bottom plate. Determine the ratio of these two shear

stresses. (5 points)

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1) c) Consider the smoke visualization of flow over a sphere in Figure below. Are we seeing

streamlines, streaklines, or pathlines? (2 points)

1) d) A stationary probe is placed in a fluid flow and measures pressure and temperature as

functions of time at one location in the flow (as shown in the figure below). Is this a

Lagrangian or Eulerian measurement? (2 points)

1) e) A crane is used to lower weight into the sea (which has a density ρsea = 1025 kg/m3)

for an underwater construction project. Determine the tension force in the rope of the

crane due to a rectangular 0.4m × 0.4m × 3m concrete block when it is (i) suspended

in the air, and (ii) completely immersed in water. (The density of the block is ρblock =

2300 kg/m3) (3 points3 points3 points3 points)

2) A closed cylindrical tank,

an inverted piping system as shown in the figure below. The liquid in the top part of the

piping system has a density

filled with water with a density

60kPa, determine: (a) the pressure in pipe B, and (

(point C in the figure below). (

, filled with water, has a hemispherical dome and is connected to


piping system has a density ρ = 800 kg/m3, and the remaining parts of the system are

density of ρwater = 1000 kg/m3. If the pressure gage reading at A is

) the pressure in pipe B, and (b) the pressure at the top of the dome

(point C in the figure below). (5 points)

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has a hemispherical dome and is connected to


, and the remaining parts of the system are

. If the pressure gage reading at A is

) the pressure at the top of the dome

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3) An open rectangular tank 1 m 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 long axis of the tank) that can develop before the gasoline would begin to spill? (10

points)

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4) The drag force FD on a washer-shaped plate placed normal to a stream of fluid can be

expressed as

FD = f(d1, d2, V, μ, ρ)

where d1 is the outer diameter, d2 the inner diameter, V the fluid velocity, μ the fluid

viscosity, and ρ the fluid density. Some experiments are to be performed in a wind tunnel

to determine the drag force. By dimensional analysis, find the dimensionless parameters

that you would use to organize these data. Express the non-dimensional form of the

functional relationship that is given above. (10 points)

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5) An open tank has a vertical partition and on one side contains gasoline with density ρgas =

700 kg/m3 at a depth of 4 m, as shown in the figure below. A rectangular gate that is 4 m

high and 2 m wide and hinged at its end is located in the partition. There is a stopper at

the top end of the gate to prevent it from opening by the effect of the gasoline. Water is

slowly added to the empty side of the tank. At what depth h, will the gate start to open?

(Take the density of the water as ρwater = 1000 kg/m3) (10 points)

fluid mechanics q3 solutions - skuleexams.skule.ca/exams/custom/20109/aer210_2010_qs... · 2018. 2....

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