If U∞ = free stream velocity, u = velocity at y, and δ = boundary layer thickness, then in a boundary layer flow, the momentum thickness θ is given by

\(\theta = \mathop \smallint \limits_0^\delta \frac{u}{{{U_\infty }}}\left( {1 - \frac{{{u^2}}}{{U_\infty ^2}}} \right)dy\)

\(\theta = \mathop \smallint \limits_0^\delta \frac{u}{{{U_\infty }}}\left( {1 - \frac{u}{{{U_\infty }}}} \right)dy\)

\(\theta = \mathop \smallint \limits_0^\delta \frac{u}{{{U_\infty }}}\left( {1 - \frac{{{u^2}}}{{U_\infty ^2}}} \right)dy\)

\(\theta = \mathop \smallint \limits_0^\delta \frac{{{u^2}}}{{U_\infty ^2}}\left( {1 - \frac{u}{{{U_\infty }}}} \right)dy\)

\(\theta = \mathop \smallint \limits_0^\delta \left( {1 - \frac{u}{{{U_\infty }}}} \right)dy\)

Flow separation in flow past a solid object is caused by

The boundary layer thickness reducing to zero.

A reduction of pressure to vapour pressure

The boundary layer thickness reducing to zero.

1.	If U∞ = free stream velocity, u = velocity at y, and δ = boundary layer thickness, then in a boundary layer flow, the momentum thickness θ is given by
A.	\(\theta = \mathop \smallint \limits_0^\delta \frac{u}{{{U_\infty }}}\left( {1 - \frac{u}{{{U_\infty }}}} \right)dy\)
B.	\(\theta = \mathop \smallint \limits_0^\delta \frac{u}{{{U_\infty }}}\left( {1 - \frac{{{u^2}}}{{U_\infty ^2}}} \right)dy\)
C.	\(\theta = \mathop \smallint \limits_0^\delta \frac{{{u^2}}}{{U_\infty ^2}}\left( {1 - \frac{u}{{{U_\infty }}}} \right)dy\)
D.	\(\theta = \mathop \smallint \limits_0^\delta \left( {1 - \frac{u}{{{U_\infty }}}} \right)dy\)
Answer» B. \(\theta = \mathop \smallint \limits_0^\delta \frac{u}{{{U_\infty }}}\left( {1 - \frac{{{u^2}}}{{U_\infty ^2}}} \right)dy\)

2.	A block of 2 kg slides on a parallel surface at a speed of 4 m/s. It falls on an unpressed spring and presses it until the block is completely motionless. The amount of kinetic friction is 15 N and the spring constant is 10,000 N/m. Spring presses with _____.
A.	5.5 m
B.	8.5 m
C.	5.5 cm
D.	8.5 cm
Answer» D. 8.5 cm

3.	For fully developed laminar flow through a circular pipe with Reynolds number Re the friction factor is
A.	Inversely proportional to Re
B.	Proportional to Re
C.	Proportional to square of Re
D.	Independent of Re
Answer» B. Proportional to Re

4.	A nozzle is fitted at the end of a pipe of length 300 m and of diameter 10 cm for transmitting water. What is the diameter of the nozzle considering maximum transmission of power through the nozzle (f = 0.009)
A.	2.6 cm
B.	2.5 cm
C.	2.4 cm
D.	2.7 cm
Answer» B. 2.5 cm

5.	If x is the distance measured from the leading edge of a flat plate, the laminar boundary layer thickness varies as
A.	\(\frac{1}{x}\)
B.	\({x^{\frac{4}{5}}}\)
C.	\(x^2\)
D.	\({x^{\frac{1}{2}}}\)
Answer» E.

6.	For laminar flow over a flat plate, the thickness of the boundary layer at a distance from the leading edge is found to be 5 mm. The thickness of the boundary layer at a downstream section, which is at twice the distance of the previous section from the leading edge, will be
A.	10 mm
B.	\(5\sqrt 2 mm\)
C.	\(\frac{5}{{\sqrt 2 }}mm\)
D.	2.5 mm
Answer» C. \(\frac{5}{{\sqrt 2 }}mm\)

7.	An incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm will be
A.	4
B.	2
C.	0.5
D.	0.25
Answer» D. 0.25

8.	A boundary is known as hydrodynamically smooth if:
A.	\(\frac{K}{\delta}=0.3\)
B.	\(\frac{K}{\delta}>0.3\)
C.	\(\frac{K}{\delta}<0.25\)
D.	\(\frac{K}{\delta}=0.5\)
Answer» D. \(\frac{K}{\delta}=0.5\)

9.	A fluid is flowing over a flat plate. At a distance of 8 cm from the leading edge, the Reynolds number is found to be 25600. The thickness of the boundary layer at this point is
A.	1.5 mm
B.	2.5 mm
C.	4.0 mm
D.	5.0 mm
Answer» C. 4.0 mm

10.	Flow separation in flow past a solid object is caused by
A.	A reduction of pressure to vapour pressure
B.	A negative pressure gradient
C.	A positive pressure gradient
D.	The boundary layer thickness reducing to zero.
Answer» D. The boundary layer thickness reducing to zero.