Mechanical Properties of Fluids

In a hydraulic lift, the pressure is $P = F_1/A_1$. To find the weight $W$ that can be lifted by the larger piston of area $A_2$, we use:

In the formula $P = F/A$, if $F$ is in Newtons and $A$ is in $m^2$, then $P$ is in:

The main advantage of hydraulic brakes over mechanical brakes is:

A hydraulic press has a mechanical advantage defined as the ratio of:

A hydraulic lift is used to support a load. If the system is in equilibrium and the input piston is at a lower height than the output piston, how does this affect the pressure balance equation?

In a hydraulic press, the ratio of the square of the radii of the pistons is $1:25$. The ratio of the pressures on the two pistons is:

What happens to the pressure at a point in an enclosed fluid if the container is moved upwards with a constant acceleration $a$?

A hydraulic system is filled with a mixture of $90\%$ oil and $10\%$ air bubbles by volume. When a pressure $P$ is applied, the air bubbles compress significantly while the oil remains mostly incompressible. How does this affect the 'responsiveness' of the system compared to a pure oil system?

An ideal liquid is contained in a pipe of varying cross-section. Two pistons are fitted at the ends. If the pressure at the small piston is increased by $\Delta P$, the pressure at the large piston will increase by:

In a hydraulic jack, the pump piston has an area $a$ and is moved by a handle with a mechanical advantage $M$. The lift piston has an area $A$. The overall mechanical advantage of the jack is:

When a spinning ball moves through the air, the velocity of air relative to the ball is different on the top and bottom. This results in a pressure difference known as:

What is the dimension of the term $\rho gh$ in Bernoulli's equation?

Which of these devices is used to spray insecticides using Bernoulli's principle?

In Torricelli's experiment, the speed of efflux does NOT depend on:

In a Venturi meter, the difference in liquid levels in the U-tube manometer is $h$. The pressure difference between the wide and narrow parts of the pipe is given by:

A liquid of density $800\text{ kg/m}^3$ flows through a horizontal pipe. At a point where the velocity is $3\text{ m/s}$, the pressure is $10000\text{ Pa}$. What is the pressure at a point where the velocity is $5\text{ m/s}$?

A large tank filled with water has two holes at depths $h$ and $4h$ from the top. What is the ratio of the velocities of efflux $v_1/v_2$ from these holes?

A spray bottle (atomizer) works on the principle that high-speed air over the top of a tube:

A liquid is flowing through a pipe with a constriction. At the constriction, the streamlines:

If the Bernoulli constant for a given flow is $C$, and the fluid density is $\rho$, what is the dimension of $C$?

Stokes' Law applies when the fluid medium is:

When we stir a beaker of water and then leave it, the water eventually comes to rest. This is due to:

In the terminal velocity state, the acceleration of the falling object is:

The coefficient of viscosity of a fluid is a measure of its:

In the formula for terminal velocity $v_t = \frac{2r^2(g)(\rho - \sigma)}{9\eta}$, what does $\sigma$ represent?

The coefficient of viscosity for an ideal fluid is:

Which physical property of a fluid is responsible for the damping of oscillations of a pendulum swinging in it?

Stokes' law is derived based on the assumption that:

The power required to move a plate of area $A$ with velocity $v$ over a layer of liquid of thickness $h$ and viscosity $\eta$ is:

Two spheres $A$ and $B$ have radii $r$ and $2r$ and densities $2\rho$ and $\rho$ respectively. They are released in a liquid of density $\rho/2$ and viscosity $\eta$. The ratio of their terminal velocities $v_A / v_B$ is:

The force on a length $dl$ on the surface of a liquid is $T \cdot dl$. The direction of this force is:

Water rises in a capillary tube. If the experiment is performed in an elevator falling freely, the water will:

When a drop of water is trapped between two glass plates, they are difficult to separate because of:

The work done in breaking a drop of radius $R$ into $n$ droplets of equal radius $r$ is:

The potential energy of a molecule on the surface of a liquid compared to one inside the liquid is:

In a capillary tube, the liquid level falls if the angle of contact is:

The work done in blowing a soap bubble from radius $R_1$ to $R_2$ is proportional to:

Which of the following is true regarding the surface energy of a liquid?

A soap bubble of radius $r_1$ is placed inside another soap bubble of radius $r_2$. The radius of a single soap bubble which would have an excess pressure equal to the pressure difference between the inside of the inner bubble and the outside of the outer bubble is:

The height of water in a capillary tube is $h$. If the tube is tilted by an angle $\alpha$ with the horizontal, the length of the water column in the tube will be:

If the force acting on a surface is doubled and the area is also doubled, the pressure will ________.

Standard temperature and pressure (STP) for gases often uses a pressure of:

A balloon filled with air is weighted so that it just floats in water. If it is pushed down slightly, it will ________.

The broad base of a high-rise building is designed to ________.

Two vessels A and B of different shapes have the same base area and are filled with water to the same height $h$. Which of the following is true?

What is the pressure at a point $100\text{ m}$ below the ocean surface? (Relative density of sea water $= 1.03$, atmospheric pressure $= 10^5\text{ Pa}, g = 10\text{ m/s}^2$)

The SI unit of pressure is Pascal (Pa). $1\text{ Pa}$ is equivalent to:

An open U-tube contains mercury. When water is poured into one limb to a height $h$, the mercury level in the other limb rises by $x$. If the density of mercury is $13.6$ times that of water, then $x$ is:

A metal block of density $\rho$ and volume $V$ is suspended by a string in a liquid of density $\sigma$. The tension in the string is:

A cylindrical tank of radius $R$ is filled with water to a height $H$. The force exerted by the water on the side wall of the tank is:

Two streamlines can intersect only when the flow is:

If the area of a pipe is $0.5 m^2$ and the fluid velocity is $10 m/s$, the volume flow rate is:

When a tap is turned on, the water stream becomes narrower as it falls. This is due to:

Which assumption is NOT necessary for the basic equation of continuity $A_1 v_1 = A_2 v_2$?

A liquid of density $\rho$ flows through a pipe of cross-section $A$ with velocity $v$. The mass of the liquid flowing out per second is:

The dimension of the volume flow rate $Av$ is:

The velocity beyond which a streamline flow becomes turbulent is called:

When a stream of water flows out of a faucet, it narrows as it falls. This is primarily due to:

For a fluid flow to be steady, the Reynolds number $Re$ must be:

A tapered pipe has a radius $r$ at the inlet and $r/n$ at the outlet. If the velocity at the inlet is $v$, find the acceleration of a fluid particle at the outlet if the pipe length is $L$. (Assume the velocity increases linearly with distance $x$ along the pipe).