Momentum changes in a fluid

In addition, the mean pressure of P + 5 (dP/d/)d/ acting on the sides of the streamtube will give rise to a force having a component [P-F (dP/d/)d/][d(dA)/d/]d/ along the 

Neglecting second order terms and noting that sin 6 = dz/dl  

Total force on fluid The rate of change of momentum of the fluid along the streamtube 

For the simple case of the incompressible fluid, p is independent of pressure, and  

Equation 2.43 is known as Bernoulli s equation, which relates the pressure at a point in the fluid to its position and velocity. Each term in equation 2.43 represents energy per unit mass of fluid. Thus, if all the fluid is moving with a velocity u, the total energy per unit mass is given by  

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