Consider a turbine extracting energy from a penstock in a dam, as in Fig. P3.171. For turbulent pipe flow (Chap. 6), the friction head loss is approximately h = CQ°, where the constant C depends on penstock dimensions and the prop- erties of water. Show that, for a given penstock geometry and variable river flow Q, the maximum turbine power pos- sible in this case is Pmax = 2P8HQ/3 and occurs when the flow rate is Q = VHI(3C). Penstock Turbine P3.171

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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Consider a turbine extracting energy from a penstock in a
dam, as in Fig. P3.171. For turbulent pipe flow (Chap. 6),
the friction head loss is approximately h = CQ°, where the
constant C depends on penstock dimensions and the prop-
erties of water. Show that, for a given penstock geometry
and variable river flow Q, the maximum turbine power pos-
sible in this case is Pmax = 2P8HQ/3 and occurs when the
flow rate is Q = VHI(3C).
Penstock
Turbine
P3.171
Transcribed Image Text:Consider a turbine extracting energy from a penstock in a dam, as in Fig. P3.171. For turbulent pipe flow (Chap. 6), the friction head loss is approximately h = CQ°, where the constant C depends on penstock dimensions and the prop- erties of water. Show that, for a given penstock geometry and variable river flow Q, the maximum turbine power pos- sible in this case is Pmax = 2P8HQ/3 and occurs when the flow rate is Q = VHI(3C). Penstock Turbine P3.171
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