previous    next

Fluids

Pressure and work

Let us consider a small stream tube in a laminar flow as depicted below.



At the place of interest the stream tube has a cross sectional area which is given by S. In the picture below we show a small displacement of the fluid in the stream tube of length Δd, displacing the fluid over a volume given by ΔV=SΔd.



We are interested to determine the amount of work ΔW which is done by the pressure P acting on the lefthand side of the displaced fluid. The pressure P acting on the lefthand side of the displaced fluid excerts a force F=SP on the displaced fluid. Hence, the work done by the pressure in order to realise the displacement Δd equals

ΔW = F×Δd = PSΔd = PΔV

We end up with the differential equation

dW/dV = P

which can only be solved when the relation P(V) is known.
For example, when P(V)=P₀ independent of the volume V, then, taking vanishing constant of integration, one has W=P₀V. But, in most cases things are not that simple.

Work has units

units of work = force×distance = Nm = J (Joule)

isobaric process