1
GATE ME 2007
MCQ (Single Correct Answer)
+2
-0.6
Which combination of the following statements about steady incompressible forced vortex flow is correct?

P: Shear stress is zero at all points in the flow.
Q: Velocity is directly proportional to the radius from the centre of the vortex.
R: Total mechanical energy per unit mass is constant in the entire flow field.
S: Total mechanical energy per unit mass is constant in the entire flow field.

A
$$P$$ and $$Q$$
B
$$R$$ and $$S$$
C
$$P$$ and $$R$$
D
$$P$$ and $$S$$
2
GATE ME 2005
MCQ (Single Correct Answer)
+2
-0.6
A leaf is caught in a whirlpool. At a given instant, the leaf is at a distance of $$120$$ $$m$$ from the centre of the whirlpool. The whirlpool can be described by the following velocitry distribution ;
$${V_r} = - \left( {{{60 \times {{10}^3}} \over {2\pi r}}} \right)m/s$$
and $${V_\theta } = - \left( {{{300 \times {{10}^3}} \over {2\pi r}}} \right)m/s.$$

Where $$r$$ (in meters) is the distance from the centre of the whirlpool . What will be the distance of the leaf from the centre when it has moved through half a revolution?

A
$$48$$ $$m$$
B
$$64$$ $$m$$
C
$$120$$ $$m$$
D
$$142$$ $$m$$
3
GATE ME 2004
MCQ (Single Correct Answer)
+2
-0.6
For a fluid flow through a divergent pipe of length $$L$$ having inlet and outlet radii of $${R_1}$$ and $${R_2}$$ respectively and a constant flow rate of $$Q,$$ assuming the velocity to be axial and uniform at any cross- section , the acceleration at the exit is
A
$${{2Q\left( {{R_1} - {R_2}} \right)} \over {\pi LR_2^3}}$$
B
$${{2{Q^2}\left( {{R_1} - {R_2}} \right)} \over {\pi LR_2^3}}$$
C
$${{2{Q^2}\left( {{R_1} - {R_2}} \right)} \over {{\pi ^2}L{R_2}^5}}$$
D
$${{2{Q^2}\left( {{R_2} - {R_1}} \right)} \over {{\pi ^2}L{R_2}^5}}$$
4
GATE ME 2004
MCQ (Single Correct Answer)
+2
-0.6
A closed cylinder having a radius $$R$$ and height $$H$$ is filled with oil of density $$\rho .$$ If the cylinder is rotated about its axis at an angular velocity of $$\omega $$ , then thrust at the bottom of the cylinder is
A
$$\pi {R^2}\,\rho gH$$
B
$$\pi {R^2} + {{\rho {\omega ^2}{R^2}} \over 4}$$
C
$$\pi {R^2} + \left( {\rho {\omega ^2}\,{R^2} + \rho gH} \right)$$
D
$$\pi {R^2}\left( {{{\rho {\omega ^2}{R^2}} \over 4} + \rho gH} \right)$$
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