Fluid is the name given to a substance which begins to flow when external force is applied on it. Shape and volume of the fluid changes by the application of very small shear stress. The branch of physics which deals the study of fluids at rest is called hydrostatics and that branch of physics which. deals with study of fluid in motion is called hydrodynamics when liquid is at rest in a container, it exerts a force on the surface of object in contact with liquid, which is always normal to the surface of object. The total normal force exerted by liquid at rest on a given surface in contact with it is called thrust of liquid on that surface.
(i) What is the cause of thrust of liquid on surface in contact?
(ii) Define hydrostatic pressure. Write its S.I. unit
(iii) Is hydrostatic pressure a vector quantity or scalar quantity? Give reason.
(iv) Define relative density of a substance
(v) What will be the measure of total preassure at a depth h below the liquid surface?
(vi) What is gauge pressure? On what factors does it depend?
(vii) What is hydrostatic paradox?

It is observed that if gravity effect is neglected the pressure at every point of liquid in equilibrium of rest is same and the increase in pressure at one point of the enclosed liquid in equilibrium of rest is transmitted equally to all other points of the liquid. This is accounted to Pascal's law. Hydraulic lift and hydraulic brakes working is based on the Pascal's law, in which a small force applied on the smaller piston will appear as a very large force on the large piston.
(i) State Pascal's law
(ii) A bottle full of a liquid is fitted with a tight cork. Explain why a slight blow on the cork may be sufficient to break the bottle?
(iii) Two Pistons of hydraulic press have diameter of 30.0 cm and 2.5 cm. Find the force exerted by longer piston when 50.0 kg wt is placed on smaller Piston.
(iv) In the above question, find the distance through which the longer piston would move after 10 strokes if the stroke of the smaller piston is 40 cm.
(v) In a car lift, compressed air exerts a force F₁ on a small piston having a radius of 5.0 cm. This pressure is transmitted to a second piston of radius 10.0 cm, If the mass of the car to be lifted is 1300 kg. Calculate F₁. What is pressure necessary to accomplish the task?

It has been found that a liquid in small quantity at rest, free from external force like gravity, always tends to have a spherical shape. Since for a given volume, a sphere has the least surface area, hence it shows that the free surface of every liquid at rest has a tendency to have a least surface area. The free surface of liquid behaves as if covered by a stretched membrane, having tension in all directions parallel to the surface. This tension in the free surface of liquid at rest is called the surface tension. It arises due to the fact that the free surface of liquid at rest has some additional potential energy.
(i) What is surface tension and its origin?
(ii) Why does oil spread over the surface of water?
(iii) At what temperature the surface tension of a liquid is zero?
(iv) Surface tension of all lubricating oils and paints is kept low. Why?
(v) What is the effect of impurities on the surface tension of liquid?
(vi) What is work done in blowing a soap bubble of radius r and surface tension S?
(vii) Define surface energy of liquid.

Stokes' Law: A body falling through a viscous medium experiences a retarding force resulting in absorption of energy by the medium in the form of heat .:The motion of the body produces a relative motion between the different layers of the fluid. Consequently, it experiences a force which tends to retard its motion. When a small spherical body is dropped in a viscous liquid such as glycerine, it accelerates first, but soon begins to experience a retarding force. When the retarding force becomes equal to the effective weight of the body in the fluid, the body experiences no net force and falls with a constant velocity known as the terminal velocity. George stokes found that a small spherical body of radius r moving with a uniform velocity v in a fluid of coefficient of viscosity \(\eta\) experiences a retarding force F given by F = \(6 \pi \eta r v\) 
(i) Define viscosity.
(ii) Define S.I unit of coefficient of viscosity of a liquid.
(iii) Name the forces which act on the small spherical body falling freely through a viscous medium.
(iv) Write the dimenslonal formula of coefficient of viscosity \(\eta\) .
(v) What would be the terminal velocity of the body if the upthrust on the body is negligible to its weight?
(vi) Write the expression for terminal velocity of spherical body of radius r and density \(\rho\) falling freely through a liquid of density \(\sigma\) and coefficient of viscosity \(\eta\).

Equation of continuity is a fundamental equation of liquid flow and is a special case of the general law of conservation of mass. Consider an incompressible and non viscous liquid flowing slowly and steadily through a pipe of non-uniform cross-section. Let A and B be two different sections of a pipe having cross-sectional area Q ₁ and Q ₂ respectively. Let v₁ and v ₂ be the respecstive velocities of the liquid flow through these cross sections. According to the equation of continuity of flow Q ₁ v₁ = Q₂V₂ or QV = constant i.e., the velocity of liquid flow at any section of the pipe is inversely proportional to area of cross-section of the pipe at that section.
(i) Water flows through a horizontal pipe of nonuniform cross-section at the rate of 31.4 litre per minute. Determien the velocity of flow of water at the section of the pipe where diameter is 2 cm.
(ii) Water flows through a horizontal pipe of diameter 2 cm at a speed of 3 cm s^-1. The pipe has a nozzle of diameter 5 mm at its end. Determine the speed of water emerging from the nozzle.
(iii) What is meant by streamline flow?
(iv) Distinguish between laminar flow and turbulent flow.
(v) Still water runs deep, why?