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_fg = 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 A₁V₁Dt = A₂V₂Dt    (as shown in figure (6))

Or A₁V₁ = A₂V₂.

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 V₁ = V₂ = 0 in the Bernoulli’s equation

P₁+rgh₁ = P₂+rgh₂.

P₁ - P₂ = rg (h₁-h₂). As expected from hydrostatics.