The linear momentum balance for a nondeforming, stationary control volume is
. Since the flow is steady, the momentum balance simplifies to
is the density of the fluid,
represents the product of the component of velocity normal to the control surface, and
is the differential area of the control surface. The velocity coming out of the turbine is determined using the continuity equation for an incompressible fluid,
. The overall force balance takes into account the pressures at the inlet and the outlet.
is the resultant force,
is the intake pressure, and
is fixed at 0 kPa for this Demonstration.