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Answer :
The power expended in maintaining the flow is 0.0249W.
B. To calculate the power expended in maintaining the flow, we can use the Hagen-Poiseuille equation, which relates pressure drop, flow rate, and resistance in a cylindrical tube:[tex]ΔP= πr 4 8μLQ[/tex]
Where:
ΔP is the pressure drop,
μ is the viscosity of the fluid (assumed constant for blood),
L is the length of the artery,
Q is the flow rate, and
r is the radius of the artery.
First, let's calculate the resistance (
R) of the artery using the formula:
[tex]4R= πr 4 8μL[/tex]
Given:
ΔP=97.9Pa
r=11.0mm=0.011m
Q=15.0mm/s=0.015m/s
Blood viscosity is approximately 0.0035Pa⋅s
L is not provided; we assume it to be 1 m for simplification.
[tex]R= π×(0.011) 4 8×0.0035×1 =1060.44Pa⋅s/m[/tex]
Now, we can use the formula for power (
P=ΔP×Q=97.9×0.015=1.4685W
Thus, the power expended in maintaining the flow is 1.4685W.
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