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The left ventricle of a resting adult’s heart pumps blood at a flow rate of 83 cm^3/s, and an average heart beat increases the pressure in the vessels by 70.5 mm Hg, the speed of the blood from zero to 29 cm/s, and the height by 10.85 cm.
a. Calculate the total power output of the left ventricle. Note that most of the power is used to increase blood pressure.

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Answer:

0.87655949325 W

Explanation:

[tex]\Delta P[/tex] = Change in pressure = 70.5 mmHg

Q = Flow rate = [tex]83\ cm^3/s[/tex]

[tex]v_f^2[/tex] = Final velocity  = 29 cm/s

[tex]\rho[/tex] = Density of blood = 1050 kg/m³

g = Acceleration due to gravity = 9.81 m/s²

[tex]\Delta h[/tex] = Height = 10.85 cm

The hydraulic head is (from Bernoulli's equation)

[tex]H=\Delta P+\dfrac{1}{2}\rho(v_f^2-v_i^2)+\rho g\Delta y\\\Rightarrow H=70.5\times 133.322+\dfrac{1}{2}1050(0.29^2-0^2)+1050\times 9.81\times 0.1085\\\Rightarrow H=10560.95775\ Pa[/tex]

Power is given by

[tex]P=HQ\\\Rightarrow P=10560.95775\times 83\times 10^{-6}\\\Rightarrow P=0.87655949325\ W[/tex]

The power output of the left ventricle is 0.87655949325 W

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