1. Water contained in a tank flows through an orifice of radius 1 cm , under a constant pressure difference of 10 cm of water column. The rate of flow of water through the orifice is
(1) 4 cm3 s-1(2) $40 cm^3 s^{-1}$(3) $440 cm^3 s^2$(4) $4400 cm^3 s^{-1}$
2. Three capillaries of internal radii 2r, 3r and 4r, all of the same length, are joined end to end. A liquid passes through the combination and the pressure difference across this combination is 20.2 cm of mercury. The pressure difference across the capillary of internal radius $2 r$ is
(1) 2 cm of Hg(2) 4 cm of Hg(3) 8 cm of Hg(4) 16 cm of Hg
3. A liquid is flowing through a narrow tube. The coefficient of viscosity of liquid is 0.1308 poise. The length and inner radius of tube are 50 cm and 1 mm respectively. The rate of flow of liquid is $360 cm^3 / min$. The pressure difference between ends of tube is
(1) $106 dyne / cm^2$(2) $10^4 dyne$(3) $10^5 dyne$(4) none of these
4. The quantity $p / L$ represents
(1) Pressure density(2) Pressure gradient(3) Force gradient(4) Viscosity gradient
5. The pressure difference is doubled across the ends of a pipe. To maintain same volume flow, the length of the pipe should
(1) Halve(2) Double(3) Become 4 times(4) $Become 1 / 4^{th}$
6. The dimensions of $(\frac{\eta L}{pr^4})$ will be
(1) [L3T-1](2) $[L^2 T^{-3}]$(3) $[L^{-3} T^1]$(4) $[L^{-2} T^3]$
7. Poiseuille's law for the liquid flow can be compared with Ohm's law for current flow. The viscosity of liquid is equivalent to
(1) Resistance(2) Resistivity(3) Conductance(4) Conductivity
8. Two capillary of length $L$ and $2 L$ and of radius $R$ and $2 R$ are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary, $X=\pi PR^4 / 8 \eta L$ )
(1) $\frac{8}{9} X$(2) $\frac{9}{8} X$(3) $5/7 X$(4) $7/5 X$
9. Two capillary tubes of same length but radii $r_{1}$, $r_{2}$ are fitted in parallel to the bottom of a vessel. The pressure head is p . What should be the radius of single tube that can replace the two tubes so that the rate of flow us same as before?
(1) $r_{1}+r_{2}$(2) $r_{1}^2+r_{2}^2$(3) $r_{1}^4+r_{2}^4$(4) None of the above
10. Two capillary of length $L$ and $2 L$ and of radius $R$ and $2 R$ are connected in series. The net rate of flow of fluid through them will be(Given rate of the flow through single capillary, $X=\frac{\pi P R^{2}}{8 \eta L}$ )
(1) $\frac{8}{9} X$(2) $\frac{9}{8} X$(3) $5/7 X$(4) $7/5 X$
11. Three capillaries of length $L$, $L / 2$ and $L / 3$ are connected in series. Their radii are $r$, $r / 2$ and $r / 3$ respectively. Then if stream-line flow is to be maintained and the pressure across the first capillary is P , then
(1) The pressure difference across the ends of second capillary is 8P(2) The pressure difference across the third capillary is 43P(3) The pressure difference across the ends of the second capillary is 16 P(4) The pressure difference across the third capillary is 59P