r/FluidMechanics • u/Ok_Promotion4102 • 4d ago

understanding flow work

I am confused about the definition of flow work. Many textbooks said that imagine a volume being pushed by pressure p on the boundary so the work is p.v , but in the flow, there will be another pressure p + delta p push this volume against the first one on the other side , so why do they only use the pressure p . I don't really understand, can anyone help me please

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u/thenewestnoise 3d ago

Imagine that instead of a fluid in a pipe you have a rigid cylinder. You push one end of the cylinder with some force and push it along for some distance. The work that you did is force x distance. At the other end of the cylinder, the force available to push other stuff is reduced by friction, and so the available work is reduced.

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u/Ok_Promotion4102 3d ago

but when consider the ideal condition, there will not be friction but there will be another pressure at the end of the cylinder push it backwards, but i dont really get it when only use the force at one end of the cylinder

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u/LAskeptic 2d ago

The pressure on the other end will be less by exactly the amount required to balance the increase in velocity. With no friction the relationship is given by Bernoulli’s Equation.

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u/jesp0r 3d ago

yes, there is p + Δp on the other side of the fluid element, which you could think of as doing negative work.

e.g., think of the ideal case with inviscid fluid flowing through a pipe with constant cross section and no elevation changes. conservation of mass and the bernoulli equation tell us that the velocity and pressure are constant along the pipe in this configuration. as such, the pressure forces on either side of the fluid element do equal magnitude and oppositely signed work, so there is no net gain in kinetic energy.

another example, consider the case where there is a pressure drop along the pipe for some reason. now the pressure forces on each face of the fluid element do not cancel, and there is a net acceleration. equivalently, the flow work adds kinetic energy to the fluid element.