Question

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.

Answer 1

0.87655949325 W

Step-by-step explanation:

`\Delta P` = Change in pressure = 70.5 mmHg

Q = Flow rate =
`83\ cm^3/s`

`v_f^2` = Final velocity = 29 cm/s

`\rho` = Density of blood = 1050 kg/m³

g = Acceleration due to gravity = 9.81 m/s²

`\Delta h` = Height = 10.85 cm

The hydraulic head is (from Bernoulli's equation)

`H=\Delta P+(1)/(2)\rho(v_f^2-v_i^2)+\rho g\Delta y\\\Rightarrow H=70.5* 133.322+(1)/(2)1050(0.29^2-0^2)+1050* 9.81* 0.1085\\\Rightarrow H=10560.95775\ Pa`

Power is given by

`P=HQ\\\Rightarrow P=10560.95775* 83* 10^(-6)\\\Rightarrow P=0.87655949325\ W`

The power output of the left ventricle is 0.87655949325 W