Head form of Bernoulli’s equation

There is no simple, universal rule for deciding when to use the head form of Bernoulli s equation and when to use the energy form, Eq. 5.7 if correctly applied, both give the same result. Through practice engineers learn which is more convenient for a given problem. 

In the head form of Bernoulli s equation, show that each term has the dimension of a length. 

If we write jthe head form of Bernoulli s equation, Eq. 5.11, between the free surface of the fluid (point 1) and the inside of the pump cylinder, there is no pump work oyer this section so... 

Equation 1.13 is simply an energy balance written for convenience in terms of length, ie heads. The various forms of the energy balance, equations 1.10 to 1.13, are often called Bernoulli s equation but some people reserve this name for the case where the right hand side is zero, ie when there is no friction and no pump, and call the forms of the equation including the work terms the extended or engineering Bernoulli equation. 

Thus, Bernoulli s equation states that the total head of the fluid is constant. Bernoulli s equation can be modified to take into acconnt the friction losses in the flnid flow to be in the form ... 

The subscript s is used in Ap, and to call attention to the fact that in Eqs. (5.7) and (5.7a) these quantities, when they are associated with the Fanning friction factor, relate only to skin friction. If other terms in the Bernoulli equation are present or if form friction is also active, p — p differs from Ap,. If boundary-layer separation occurs, hf is greater than hf. The last term in Eq. (5.7), which includes the friction factor, is written in a manner to show the relation of to the velocity head V j2g. ... 

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