2. (15 points) Each time the heart beats, it does work to pump blood out of the

Question

2. (15 points) Each time the heart beats, it does work to pump blood out of the left ventricle into the aorta. The average heart beats 70 Watt (J/s; power). times per minute, and you can assume that the rate of work done by the heart is I The pumping heart does work to move blood through the aortic valve connecting the left ventricle to the aorta, but some of the energy is also lost through friction in the valve. Assume that the rate of frictional energy loss in the aortic valve s proportional to velocity/ = Bu, where B-0.7 kg-m/s2.

Explanation / Answer

Rate of work done by heart = Change in KE + Change in PE + Change in internal energy + Friction losses

Assuming blood remains at same vertical level, Change in PE=0

Assuming there is no change in temperature of blood, and making simple assumptions, Change in internal energy=0

Thus,

Rate of work done by heart = Increase in Kinetic enegy + Friction loss

Numerically,

Rate of work done by heart = 0.5 x (mass flow rate ) * v2 + B*v

1 Watt = 0.5 x 0.1 x v2 + 0.7 v

Thus, 0.05v2 + 0.7v - 1=0

Solving, we get

v= 1.3067 m/s --- Answer

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