Two capillaries of same length but different radii $r_1$ and $r_2$ are connected in series. The pressure difference across the first capillary is $\Delta P_1$ and across the second is $\Delta P_2$. If the rate of flow of liquid through the combination is $Q$, and $r_1 = 2r_2$, then the ratio $\Delta P_1/\Delta P_2$ is:

A water tank, open to the atmosphere, has a leak in it, in the form of a circular hole, located at a height h below the open surface of water. The velocity of the water coming out of the hole is

A cylinder drum, open at the top, contains 15 L of water. It drains out through a small opening at the bottom. 5 L of water comes out in time ${t_1}$, the next 5 L in further time ${t_2}$ and the last 5 L in further time ${t_3}$. Then

If the radius of a tube is doubled, while keeping all other factors constant, how will the flow rate of a liquid through the tube change according to Poiseuille's equation?

The level of water in a tank is 5 m high. A hole of area $10{\rm{c}}{{\rm{m}}^2}$ is made in the bottom of the tank. The rate of leakage of water from the hole is

The radius of a blood vessel is doubled. Assuming all other factors remain constant, according to Poiseuille's equation, the rate of blood flow through the vessel will become:

The level of water in a tank is 5 m high. A hole of area $10{\rm{c}}{{\rm{m}}^2}$ is made in the bottom of the tank. The rate of leakage of water from the hole is

Which of the following factors does NOT directly affect the flow rate of a liquid according to Poiseuille's equation?

A tank of height $H$ is fully filled with water. If the water rushing from a hole made in the tank below the free surface, strikes the floor at maximum horizontal distance, then the depth of the hole from the free surface must be

A viscous liquid flows through a horizontal pipe of varying cross-section. At point A, the radius is 'r' and the velocity is 'v'. At point B, the radius is 'r/2'. Ignoring any energy losses due to viscosity, what is the pressure difference between points A and B?

A large open tank has two holes in its wall. One is a square hole of side a at a depth of $x$ from the top and the other is a circular hole of radius r at a depth $4x$ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then r is equal to