The Darcy–Weisbach equation states that the power-generating capacity in a hydroelectric system that is lost due to head loss is given by P = ηγQH, where η is the efficiency of the turbine, γ is the specific gravity of water, Q is the flow rate, and H is the head loss. Assume that η = 0.85 ± 0.02, H = 3.71 ± 0.10 m, Q = 60 ± 1m³/s, and γ = 9800 N/m³ with negligibleuncertainty.a) Estimate the power loss (the units will be in watts), and find the uncertainty in the estimate.b) Find the relative uncertainty in the estimated power loss.c) Which would provide the greatest reduction in the uncertainty in P: reducing the uncertainty in η to 0.01, reducing the uncertainty in H to 0.05, or reducing the uncertainty in Q to 0.5?
The Darcy–Weisbach equation states that the power-generating capacity in a hydroelectric system that is lost due to head loss is given by P = ηγQH, where η is the efficiency of the turbine, γ is the specific gravity of water, Q is the flow rate, and H is the head loss. Assume that η = 0.85 ± 0.02, H = 3.71 ± 0.10 m, Q = 60 ± 1m³/s, and γ = 9800 N/m³ with negligible
uncertainty.
a) Estimate the power loss (the units will be in watts), and find the uncertainty in the estimate.
b) Find the relative uncertainty in the estimated power loss.
c) Which would provide the greatest reduction in the uncertainty in P: reducing the uncertainty in η to 0.01, reducing the uncertainty in H to 0.05, or reducing the uncertainty in Q to 0.5?
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