1
GATE ME 2005
+2
-0.6
A venturimeter of $$20$$ $$mm$$ throat diameter is used to measure the velocity of water in a horizontal pipe of $$40$$ $$mm$$ diameter. If the pressure difference between the pipe and throat sections is found to be $$30$$ $$kPa$$ then, neglecting frictional losses, the flow velocity is
A
$$0.2$$ $$m/s$$
B
$$1$$ $$m/s$$
C
$$1.4$$ $$m/s$$
D
$$2.0$$ $$m/s$$
2
GATE ME 2005
+2
-0.6
A $$U$$-tube manometer with a small quantity of mercury is used to measure the static pressure difference between two locations $$A$$ and $$B$$ in a conical section through which an incompressible fluid flows. At a particular flow rate, the mercury column appears as shown in the figure. The density of mercury is $$13600$$ $$kg/{m^3}$$ and $$g = 9.81$$ $$m/{s^2}.$$ Which of the following is correct?
A
Flow direction is $$A$$ to $$B$$ & $${P_A} - {P_B} = 20\,kPa$$
B
Flow direction is $$B$$ to $$A$$ & $${P_A} - {P_B} = 1.4\,kPa$$
C
Flow direction is $$A$$ to $$B$$ & $${P_B} - {P_A} = 20\,kPa$$
D
Flow direction is $$B$$ to $$A$$ & $${P_B} - {P_A} = 1.4\,kPa$$
3
GATE ME 2003
+2
-0.6
A water container is kept on a weighing balance. Water from a tap is falling vertically into the container with a volume flow rate of $$'Q'$$; the velocity of the water when it hits the water surface is $$'U'$$. At a particular instant of time the total mass of the container and water is $$'m'.$$ The force registered by the weighing balance at this instant of time is
A
$$mg + \rho \,QU$$
B
$$mg + 2\,\rho \,QU$$
C
$$mg + \,\rho \,Q{U^2}/2$$
D
$$\rho \,Q{U^2}/2$$
4
GATE ME 2003
+2
-0.6
Air flows through a venture and into atmosphere. Air density is $$\rho$$; atmospheric pressure is $$'\,{P_a}';$$ throat diameter is exit diameter is $$'{D_t}';$$ and exit velocity is $$U.$$ the throat is connected to a cylinder containing a frictionless piston attached to a spring. The spring constant is $$'k'.$$ the bottom surface of the piston is exposed to atmosphere. Due to the flow, the piston moves by distance $$x.$$ assuming incompressible frictionless flow, $$x$$ is
A
$$\left( {\rho {U^2}/2k} \right)\pi {D_s}^2$$
B
$$\left( {\rho {U^2}/8k} \right)\left( {{{{D^2}} \over {{D_t}^2}} - 1} \right)\pi {D_s}^2$$
C
$$\left( {\rho {U^2}/2k} \right)\left( {{{{D^2}} \over {{D_t}^2}} - 1} \right)\pi {D_s}^2$$
D
$$\left( {\rho {U^2}/8k} \right)\left( {{{{D^4}} \over {{D_t}^4}} - 1} \right)\pi {D_s}^2$$
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