Question

Consider a small Pelton wheel hydro turbine, with a total head (reservoir surface to nozzle elevation difference) of Ht = 200 ft. The flowrate to the turbine is 185 gal/s. If the pipe (penstock) feeding the turbine has a length of 1000 ft, a diameter of 19.6 in, and a friction factor of f = 0.005, determine the percent of total head lost in the pipe (penstock). Submit your answer as a percentage but without the percent symbol. ***NOTE: The value of the friction factor f is consistent with the definition in our textbook (and may differ from other textbooks). Using our textbook's notation, you could also use f' = 4f = 0.02.***

Answer 1

First, we have to calculate the velocity of flow

Discharge is given as here Q is discharge, A is area and V is velocity.

Substitute 185gal/s(29.70ft³/s)for Q and for A, here D is diameter 19.6in (1.633ft)

V= 14.183ft/sec

Head loss due to friction is given by equation

Here f is friction factor, l is length of pipe, V is velocity, D is diameter, g is acc due to gravity

Substitute 0.02 for 4f,1000ft for l, 14.183ft/s for velocity, 1.633ft for diameter 32.174 for g

ft

percentage of total head loss

H is total head 200ft

=19.15%

Ans 19.15