Download FLUID MECHANICS Q3 Solutions

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AER210 VECTOR CALCULUS and FLUID MECHAICS
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 mሶ = 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
3 points)
points
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2) A closed cylindrical tank,, filled with water, has a hemispherical dome and is connected to
an inverted piping system as shown in the figure below. The liquid in the top part of the
piping system has a density ρ = 800 kg/m3, and the remaining parts of the system are
filled with water with a density of ρwater = 1000 kg/m3. If the pressure gage reading at A is
60kPa, determine: (a)) 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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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)
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