Bernoulli’s Theorem
It states that in a steady state, ideal flow of an incompressible fluid, the total energy at any point of the fluid is constant. The total energy consists of pressure energy, Kinematic energy and potential energy or datum energy.
p1 + v1 + z1 = p2 + v2 + z2 + hL
Assumptions:
a. The fluid is ideal, i.e. viscosity is zero
b. The flow is steady
c. The flow is incompressible
d. The flow is irrotational
Bernoulli’s Equation for Real Fluid:
The Bernoulli’s equation was derived on the assumption that fluid is inviscid (non-viscous) and therefore frictionless. But all the real fluids are viscous and hence offer resistance to flow. Thus there are always some loses in fluid flows and hence in the application of Bernoulli’s equation, these loses have to be taken into consideration. Thus the Bernoulli’s equation for real fluids between point 1 and 2 is given by
p1 + v1 + z1 = p2 + rg 2g rg 2g
where hL is loss of energy between point 1 and 2.
Practical Applications of Bernoulli’s Equation:
Bernoulli’s equation is applied in all problems of incompressible fluid flow where energy considerations are involved.
- Venturimeter.
- Orifice meter
- Pitot-tube
Venturimeter and Orifice Meter:
Both the devices are used for measuring the rate of a flow of a fluid flowing through a pipe.
Pitot Tube:
It is a device used for measuring the velocity of flow at any point in a pipe or a channel.
