Quiz two solutions ME 390, L. S. Caretto, Spring 2007 Page   College of Engineering and Computer Science Mechanical Engineering De

Solution to Quiz Seven – Momentum and Energy Equations

Water is supplied at 150 ft³/s and 60 psi to a hydraulic turbine through a 3-ft inside diameter pipe as indicated in the figure at the right.  The turbine discharge pipe has a 4-ft inside diameter.  The static pressure at section (2), 10 ft below the turbine inlet, is 10-in Hg vacuum.  If the turbine develops 2500 hp determine the power lost between sections (1) and (2).

The energy equation gives the head loss between the inlet, i, (section 1) and outlet, o, (section 2).    

Multiplying this equation by the mass flowrate times gravity, , and changing subscripts to 1 as inlet and 2 as outlet gives the power input and loss. 

We know that z₂ – z₁ = –10 ft and we can find the velocities at points 1 and 2 as V = Q/A. 

The pressure at point 1 is 60 psi = (60 psi)(144 psi/psf) = 8640 psf.  The gage pressure at point 2 is –10 in Hg = (–10 in Hg)(70.726 psf/inHg) = –707.3 psf.  The turbine power output of 2500 hp represents an input of –2500 hp.  Substituting the data found above into the energy equation and solving for the loss gives. 

= 301.6 hp