When a body floats in a fluid, the magnitude Fb of the buoyant force on the body is equal to the magnitude Fg of the gravitational force on the body.
Thus, Fb = Fg (floating).
Also, Fb = mfg = Fg.
Where, mf = 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.
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 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,
Application of Bernoulli’s Equation:
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.