1
GATE ME 2009
MCQ (Single Correct Answer)
+2
-0.6
You are asked to evaluate assorted fluid flows for their suitability in a given laboratory application. The following three flow choices. Expressed in terms of the two - dimensional velocity fields in the $$x-$$ $$y$$ plane, are made available.
$$P:$$ $$u = 2y,\,\,\,v = - 3x$$
$$Q:$$ $$u=3xy,$$ $$\,\,\,\,$$$$v=0$$
$$R:$$ $$u=-2x,$$ $$\,\,\,\,$$$$v=2y$$

Which flows should be recommended when the application requires the flow to be incompressible and irrotational?

A
$$P$$ and $$R$$
B
$$R$$ only
C
$$Q$$ and $$R$$
D
$$R$$ only
2
GATE ME 2009
MCQ (Single Correct Answer)
+2
-0.6
Consider steady, incompressible and irrotational flow through a reducer in a horizontal pipe where the diameter is reduced from $$20cm$$ to $$10cm.$$ The pressure in the $$20cm$$ pipe just upstream of the reducer is $$150kPa.$$ The fluid has a vapour pressure of $$50kPa$$ and a specific weight of $$5\,\,kN/{m^3}.$$ Neglecting frictional effects, the maximum discharge (in $${m^3}/s$$) that can pass through the reducer without causing cavitation is
A
$$0.05$$
B
$$0.16$$
C
$$0.27$$
D
$$0.38$$
3
GATE ME 2009
MCQ (Single Correct Answer)
+1
-0.3
The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is given by the expression. $$$u\left( r \right) = {{ - {R^2}} \over {4\mu }}\left( {{{dp} \over {dx}}} \right)\left( {1 - {{{r^2}} \over {{R^2}}}} \right)$$$
Where $${{dp} \over {dx}}$$ is a constant.

GATE ME 2009 Fluid Mechanics - Laminar Flow Question 20 English

The average velocity of fluid in the pipe is

A
$${{ - {R^2}} \over {8\mu }}\left( {{{dp} \over {dx}}} \right)$$
B
$${{ - {R^2}} \over {4\mu }}\left( {{{dp} \over {dx}}} \right)$$
C
$${{ - {R^2}} \over {2\mu }}\left( {{{dp} \over {dx}}} \right)$$
D
$${{ - {R^2}} \over \mu }\left( {{{dp} \over {dx}}} \right)$$
4
GATE ME 2009
MCQ (Single Correct Answer)
+2
-0.6
Water at $${25^0}C$$ is flowing through a $$1.0km$$ long $$G.I.$$ pipe of $$200mm$$ diameter at the rate of $$0.07$$ $${m^3}/s.$$ If value of Darcy friction factor for this pipe is $$0.02$$ and density of water is $$1000\,\,kg/{m^3}$$, the pumping power (in $$kW$$) required to maintain the flow is
A
$$1.8$$
B
$$17.4$$
C
$$20.5$$
D
$$41.0$$
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