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Bernoulli Equation

The Bernoulli Equation:-

is basically conservation of energy along a pipe. It can be written in different ways by converting energy to head (Kinsky) or pressure, etc.

Bernoulli's equation says in an ideal situation, the TOTAL HEAD = constant.
There are assumptions; An ideal fluid (no friction) flowing steadily:-
  • The fluid is incompressible and nonviscous.
  • There is no energy loss due to friction between the fluid and the wall of the pipe.
  • There is no heat energy transferred across the boundaries of the pipe to the fluid as either a heat gain or loss.
  • There are no pumps in the section of pipe under consideration.
  • The fluid flow is laminar and steady state.
Pressure in a fluid is like the energy per unit volume (energy density). From the definition of pressure:

Here is the Bernoulli equation in terms of energy per unit volume;
Note that this correponds exactly with the conservation of energy equation. Where pressure = spring energy, velocity = kinetic energy and height = potential energy.
SE1 + KE1 + PE1= SE2 + KE2 + PE2

Where: PE1 = mgh1 and KE1 = 0.5mv12 and SE1 = 0.5kx12

Total Head (also called Total Dynamic Head) is the sum of the three components; pressure head, velocity head and potential head. From the above equation, divide by g. Head is a simple way to think of each term (pressure, velocity and height) in terms of the number of METRES of that fluid it is equivalent to.
  • All terms are head (m), which is measured in the working fluid. 
  • You can use gauge or absolute pressure throughout, but gauge is normal
  • Continuity equation is also true (and often needed to solve the question)
  • Ideal fluid is assumed (no friction)
Bernouli's Equation requires velocity. This is usually found using the continuity equation.
 = V / t  =   A
Since most pipes are round, this gives;
v1d2/4 = v2d2/4

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