A hydraulic turbine-generator unit placed at the bottom of a 75-m-high dam accepts water at a rate of 1020 L/s and produces 630
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Answer:
hello attached is the free body diagram of the missing figure
Fr =
Explanation:
Average velocity is constant i.e V1 = V2 = V
The momentum equation for the flow in the Z - direction can be expressed as
-Fr + P1 Ac - P2 Ac = mB2V2 - mB1V1 ------- equation 1
Fr = horizontal force on the bolts
P1 = pressure of fluid at entrance
V1 = velocity of fluid at entrance
Ac = cross section area of the pipe
P2 and V2 = pressure and velocity of fluid at some distance
m = mass flow rate of fluid
B1 = momentum flux at entrance , B2 = momentum flux correction factor
Note; average velocity is constant hence substitute V for V1 and V2
equation 1 becomes
Fr = ( P1 - P2 ) Ac + mV ( 1 - 2 )
Fr = ( P1 - P2 ) Ac - mV ---------------- equation 2
equation for mass flow rate
m = <em>p</em>AcV
<em>p</em> = density of the fluid
insert this into equation 2 EQUATION 2 BECOMES
Fr = ( P1 - P2) Ac - <em>p</em>AcV^2
= Ac [ (P1 - P2) - pV^2 ] ---------- equation 3
Note Ac =
Equation 3 becomes
Fr = [ (P1 -P2 ) - pV^2 ] ------- relation for the horizontal force acting on the bolts
