**FLOATING: **

When a body floats in a fluid, the magnitude F_{b} of the buoyant force on the body is equal to the magnitude F_{g} of the gravitational force on the body.

Thus, F_{b} = F_{g} (floating).

Also, F_{b} = m_{f}g = F_{g}.

Where, m_{f} = mass of the fluid that is displaced by the body.

**APPERENT WEIGHT IN A FLUID: **

If an object is placed inside a fluid then,

(Apparent weight) = (Actual weight) – (Buoyant force).

**FLOW OF IDEAL FLUIDS: **

An ideal fluid is incompressible and lacks viscosity, and its flow is steady and irrotational. A stream line is the path followed by an individual fluid particle.

**EQUATION OF CONTINUITY: **

It means that total mass of fluids going into the tube through any cross-section should be equal to the total mass coming out of the same tube from any other cross section in the same time.

Fig (6)

Thus A_{1}V_{1}Dt = A_{2}V_{2}Dt (as shown in figure (6))

Or A_{1}V_{1} = A_{2}V_{2}.

The product of the area of cross section and the speed remains the same at all points of a tube of flow. This is called the “equation of continuity” and expresses the law of conservation of mass in fluid dynamics.

**BERNOULLI’S EQUATION: **

Bernoulli’s equation relates the speed of a fluid at a point the pressure at that point and the height of that point above a reference level. It is just the application of work-energy theorem in the case of fluid flow.

We here consider the case of irrotational and steady flow of an incompressible and non viscous liquid.

According to Bernoulli’s Equation,

= Constant.

**Application of Bernoulli’s Equation: **

**a) Hydrostatics: **

If the speed of the fluid is zero every where, we get the situation of hydrostatics. Putting V_{1} = V_{2} = 0 in the Bernoulli’s equation

P_{1}+rgh_{1} = P_{2}+rgh_{2}.

P_{1} - P_{2} = rg (h_{1}-h_{2}). As expected from hydrostatics.