Deck 15: Fluid Dynamics and Aerodynamics

Question 1

An aircraft flies at an altitude of 20,000 m. With what speed would it fly if M = 1?
(A) 305 m/s
(B) 300 m/s
(C) 295 m/s
(D) 290 m/s

Answer 1

AN AIRCRAFT FLIES AT AN ALTITUDE OF 20,000 M. WITH WHAT SPEED WOULD IT FLY IF M = 1?

Question 2

$\text {In the region near the wall where \(\overline { u ^ { \prime } v ^ { \prime } }\) is constant, if \(\bar { u } ( y ) = c _ { 1 } \ln y + c _ { 2 }\) (see Example \(7.8\) ), the }$$\text {eddy viscosity \(\eta\) is proportional to:}$
(A) $\ln y$
(B) $y$
(C) $y ^ { - 1 }$
(D) $y ^ { 2 }$

Answer 2

B
$y$
$\text {Refer to Eq. 7.6.8 and find}$
$$\overline { u ^ { \prime } v ^ { \prime } } = \eta \frac { d \bar { u } } { d y } . \quad \text { Const } = \eta \frac { c _ { 1 } } { y } . \quad \therefore \eta = c y$$

Question 3

$\text {A large dirigible measures \(18 \mathrm {~m}\) in diameter and is \(100 \mathrm {~m}\) long. The thin boundary layer can}$ $\text {be assumed to be developing on a flat plate with thickness at the leading edge. The drag}$ $\text {contributed by the shear stress due to the boundary layer for a dirigible speed of \(10 \mathrm {~m} / \mathrm { s }\) is}$$\text { approximately:}$
(A) $\delta = 3.6 \sqrt { v x / U _ { \infty } }$
(B) $\delta = 3.3 \sqrt { \nu x / U _ { \infty } }$
(C) $\delta = 3 \sqrt { v x / U _ { \infty } }$
(D) $\delta = 2.8 \sqrt { v x / U _ { \infty } }$

Answer 3

C
$675 \mathrm {~N}$
$\text {First, let's find \(R _ { L } : R _ { L } = U _ { \infty } L / v = 10 \times 100 / 1.5 \times 10 ^ { - 5 } = 6.67 \times 10 ^ { 7 }\). An approximation}$ $\text {to the drag can be found using Eq. 8.6.29:}$
$$F _ { D } = \frac { 1 } { 2 } \rho U _ { \infty } ^ { 2 } L w C _ { f } = \frac { 1 } { 2 } \times 1.2 \times 10 ^ { 2 } \times 100 \times ( 2 \pi \times 9 ) \times 0.073 \left( \frac { 10 \times 100 } { 1.5 \times 10 ^ { - 5 } } \right) ^ { - 0.2 } = \underline { 675 \mathrm {~N} }$$

Question 4

Question 5

A traffic flow on a freeway is very dense and it is proposed that possibly a fluid flow could simulate the flow. If it was decided to study the feasibility of the proposal, which flow would
Be a possibility?
(A) An incompressible flow
(B) A compressible flow with M < 1
(C) A compressible flow with M > 1
(D) A compressible flow with M = 1

Question 6

The free-stream flow outside a boundary layer is:

A) Either laminar or turbulent, depending on the Reynolds number
B) A smooth flow free of disturbances
C) An irrotational flow
D) Neither laminar nor turbulent

Question 7

$\text {If an irrotational vortex approximates the air flow in a tornado, the highest possible velocity,}$ $\text {assuming an incompressible flow with \(p _ { \text {atm } } = 100 \mathrm { kPa }\), is nearest:}$
(A) $400 \mathrm {~m} / \mathrm { s }$
(B) $350 \mathrm {~m} / \mathrm { s }$
(C) $300 \mathrm {~m} / \mathrm { s }$
(D) $250 \mathrm {~m} / \mathrm { s }$

Question 8

In which one of the following flows must compressibility be considered?

A) Flow around a commercial jet at takeoff
B) A category 5 hurricane
C) A Corvette at full-throttle on the Salt Lake Flats
D) Flow around the wing of a commercial aircraft in its approach to an airport

Question 9

A tall cell-phone tower is 12 cm in diameter over much of the height. A wind blows at 25 m/s. The frequency of the vortices being shed from the tower is nearest:

A) 44 Hz
B) 33 Hz
C) 22 Hz
D) 0 Hz

Question 10

To determine boundary-layer characteristics on a body, for example the boundary-layer thickness, we must first know the potential-flow solution. The information used from the
Potential-flow solution is:
(A) The lift and drag acting on the body
(B) The pressure and velocity at the boundary of the body
(C) The shearing stress acting on the boundary of the body
(D) The normal and shearing stress acting on the boundary of the body

Question 11

A bomb blast sends a shock wave through the 20 $$20 ^ { \circ } \mathrm { C }$$ C atmosphere. At a certain location, the shock wave is travelling at M = 3. The induced velocity behind the wave is nearest:

A) 760 m/s
B) 620 m/s
C) 540 m/s
D) 410 m/s

Question 12

A smooth 10-cm-diameter sphere weighs 6 N. If it is dropped in 5 $5 ^ { \circ } \mathrm { C }$ C water, its terminal velocity will be nearest:

A) 0.66 m/s
B) 0.95 m/s
C) 6.5 m/s
D) 10.5 m/s

Question 13

River water flows around circular 20-cm-diameter pier at 0.01 m/s. the flow is:

A) Creeping flow
B) Flow with a wake
C) Stokes flow
D) Low-Reynolds-number flow

Question 14

Select the incorrect statement for an inviscid flow.
(A) The drag on a body in an inviscid flow is zero
(B) The lift on a streamlined body can be approximated by neglecting viscous effects
(C) The velocity distribution in the wake of a body can be approximated by neglecting viscous effects
(D) The normal velocity component at the boundary of a body in an inviscid flow is zero

Question 15

$\text {A line source of strength \(2 \mathrm {~m} ^ { 2 } / \mathrm { s }\) is superposed with a velocity of \(8 \mathrm {~m} / \mathrm { s }\) producing along-}$$\text {slender body that resembles the one shown. The thickness \(h\) of the body is nearest:}$
(A) $15 \mathrm {~cm}$
(B) $20 \mathrm {~cm}$
(C) $25 \mathrm {~cm}$
(D) $30 \mathrm {~cm}$

Question 16

$\text {If the straight-line approximation \(u = U _ { \infty } y / \delta\) to the velocity profile is used, the boundary-}$$\text {layer thickness for a zero-pressure gradient flow on a flat plate would be approximated to be:}$
(A) $15 \mathrm {~cm}$
(B) $20 \mathrm {~cm}$
(C) $25 \mathrm {~cm}$
(D) $30 \mathrm {~cm}$

Question 17

$\text {If the velocity potential in an inviscid flow is given by \(\phi = A y\), where \(\mathrm { A }\) is a constant, the}$ $\text {stream function is:}$
(A) $- A y ^ { 2 } + B$
(B) $A x ^ { 2 } + B$
(C) $A y + B$
(D) $- A x + B$

Question 18

A farmer is using a tank of 20 $20 ^ { \circ } \mathrm { C }$ C nitrogen pressurized to 540 kPa absolute. It exits the tank out a hose. The hose snaps and the farmer is hit with the expanding nitrogen. Air is primarily
Nitrogen so assuming it is air flowing with no losses, the temperature of the exiting nitrogen is
Nearest:

A) $-120^{\circ} \mathrm{C}$
B) $-90^{\circ} \mathrm{C}$
C) $-70^{\circ} \mathrm{C}$
D) $-50^{\circ} \mathrm{C}$

Question 19

The drag on a blunt object is due primarily to:
(A) The relatively high pressure on the front of the object
(B) The wake region
(C) The shear stress acting on the front and rear of the object
(D) The separated region

Question 20

A cyclist, traveling 12 m/s, wears a helmet that is close to being a 36-cm-diameter sphere. The drag force acting on that helmet is approximately:

A) 1.8 N
B) 2.6 N
C) 3.2 N
D) 3.8 N

Question 21

Water at 20 $$20 ^ { \circ } \mathrm { C }$$ C flows between 80-cm-wide horizontal parallel plates 12 mm apart such that a pressure drop of 100 Pa occurs over a distance of 2 m. If the top plate is moving at 1.8 m/s in
The direction of the flow, the flow rate is nearest: (A) $0.0144 \mathrm {~m} ^ { 3 } / \mathrm { s }$
(B) $0.0104 \mathrm {~m} ^ { 3 } / \mathrm { s }$
(C) $0.0084 \mathrm {~m} ^ { 3 } / \mathrm { s }$
(D) $0.0054 \mathrm {~m} ^ { 3 } / \mathrm { s }$

Question 22

If the average velocity in the pipe of Number 2 is 5 m/s, the energy grade line would increase suddenly at the pump a distance nearest:

A) 1 m
B) 2 m
C) 4 m
D) 6 m

Question 23

A pressure drop of 200 kPa is measured over a 50-m-length of 2-mm-diameter pipe trans- porting 30 $$30 ^ { \circ } \mathrm { C }$$ C water. If a laminar flow exists, the flow rate is nearest:

A) 0.00195 L/s
B) 0.00243 L/s
C) 0.00732 L/s
D) 0.00991 L/s

Question 24

A square smooth conduit, 80 cm on a side, circulates 35 $$35 ^ { \circ } \mathrm { C }$$ C air in a large building. The pressure drop over a 50-m length of the horizontal conduit is not to exceed 800 Pa. Assume an average
Pressure in the conduit of 120 kPa. The maximum flow rate in the conduit is nearest: (A) $37 \mathrm {~m} ^ { 3 } / \mathrm { s }$
(B) $29 \mathrm {~m} ^ { 3 } / \mathrm { s }$
(C) $18 \mathrm {~m} ^ { 3 } / \mathrm { s }$
(D) $11 \mathrm {~m} ^ { 3 } / \mathrm { s }$

Question 25

The equation (7.3.20) for the head loss is valid for both laminar and turbulent flows. We wish to pump the flow rate Q through a long pipe of diameter D, to be selected. The head loss is
Proportional to what power of D, assuming a constant friction factor? (A) $D ^ { - 2 }$
(B) $D ^ { - 3 }$
(C) $D ^ { - 4 }$
(D) $D ^ { - 5 }$

Question 26

Oil separates a 20-mm-diameter rotating shaft from its 20.5-mm-diameter bearing. The bearing is 80 cm long and the shaft rotates at 2000 rpm. The velocity gradient at the bearing
Surface is nearest:

A) 6840 m/s/m
B) 7260 m/s/m s
C) 8040 m/s/m
D) 9406 m/s/m

Question 27

One liter of $$20 ^ { \circ } \mathrm { C }$$ C water is collected from a 60-cm-long, 4-mm-diameter tube over a time span of 4 minutes. The length of the entrance region is nearest:

A) 15 cm
B) 25 cm
C) 35 cm
D) 45 cm

Question 28

Question 29

$\text {It is desired to transport \(4 \mathrm {~m} ^ { 3 } / \mathrm { s }\) of water through a rectangular finished concrete canal that can}$$\text { be at most \(2 \mathrm {~m}\) wide. The slope of the land through which it passes is \(0.0004\). What depth of}$ $\text {water should be expected?}$

A) 1.01 m
B) 1.28 m
C) 1.44 m
D) 1.83 m

Question 30

$\text {Water at \(20 ^ { \circ } \mathrm { C }\) is transported in a 10 -cm-diameter cast iron horizontal pipe at a flow rate of}$$\text { \(0.02 \mathrm {~m} ^ { 3 } / \mathrm { s }\). The pressure drop over \(100 \mathrm {~m}\) of the pipe is nearest:}$
(A) $97 \mathrm { kPa }$
(B) $84 \mathrm { kPa }$
(C) $62 \mathrm { kPa }$
(D) $51 \mathrm { kPa }$

Question 31

$\text {The pressure drop in \(10 \mathrm {~m}\) of a turbulent flow in a pipe is \(200 \mathrm {~Pa}\). The time-average velocity,}$ $\text {in the pipe at three radial locations, is measured to be:}$
$$\begin{array} { c c c c } \bar { u } ( \mathrm {~m} / \mathrm { s } ) & 7.24 & 7.07 & 6.72 \\r ( \mathrm {~mm} ) & 23 & 25 & 27\end{array}$$
$\text {The eddy viscosity at \(r = 25 \mathrm {~mm}\) is nearest (neglect the kinematic viscosity):}$
(A) $0.00163 \mathrm {~m} ^ { 2 } / \mathrm { s }$
(B) $0.00181 \mathrm {~m} ^ { 2 } / \mathrm { s }$
(C) $0.00192 \mathrm {~m} ^ { 2 } / \mathrm { s }$
(D) $0.00227 \mathrm {~m} ^ { 2 } / \mathrm { s }$

Question 32

The shear velocity in the 60-mm-diameter horizontal water pipe of Problem 2 is nearest:

A) 0.031 m/s
B) 0.024 m/s
C) 0.019 m/s
D) 0.017 m/s

Question 33

The horsepower required to rotate the shaft of Problem 2, if SAE-30 oil at 40 $$40 ^ { \circ } \mathrm { C }$$ ills the gap, is nearest:

A) 0.203 hp
B) 0.191 hp
C) 0.174 hp
D) 0.123 hp