1.22. BIO How many times does a human heart beat during a person's lifetime? How many gallons of blood does it pump? (Estimate that the heart pumps 50 cm of blood with each beat.)

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The human heart is a powerful and reliable pump. Each day it takes in and discharges about 7500 L of blood. Suppose the work done is equal to that required for lifting this blood a height of 1.292m and that the blood density is that of water, 1.00x10^3 kg/m^3. a) What work in joules is done by the heart in a day? b) What is its power output in watts? c) At a food conversion efficiency of 7.44%, how many food calories ( one food calorie=4190 joules) must be taken from the daily diet for the heart?

In humans,blood flows from the heart to the aorta, from which itpasses into the major arteries. These branch into the smallarteries, which in turn branch into billions of tiny capillaries.Then blood then returns to the heart via the veins. The radius ofthe aorta is about 1.2cm, and the blood passes through it with aspeed of about 40cm/s. A typical capillary has a radius of about4x10-4 cm, and the blood flows through it at a speed of 5x10-2cm/s.

(a) Estimate the number of capillaries in the body.

(b) If the body contains about 5.5 litres of blood how long does ittake for the blood to circulate completely through the body. (1litre = 10cmx10cmx10cm)

Your heart pumps blood into your aorta. The maximum flow rateinto the aorta is about 500 cm3 s-1. Assume the aorta has diameter2.5 cm, that the flow is laminar, and that the blood is a Newtonianfluid with viscosity equal to that of water (1 cP). (Note theseassumptions are rather poor.)
a) Find the pressure drop per unit length along the aorta. Expressyour answer in SI units. Compare that pressure drop along a 10 cmsection of aorta with atmospheric pressure (105 Pa).
b) How much power does the heart expend just pushing blood along a10 cm section of aorta? Compare your answer with your basalmetabolic rate, about 100 W, and comment.
c) The fluid velocity in laminar pipe flow is zero at the walls ofthe pipe and maximum at the center. Sketch the velocity as afunction of distance, , from the center. Fine the velocity at thecenter. [Hint: The total volume flow rate, which you are given,equal .]

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1.22. BIO How many times does a human heart beat during a person's lifetime? How many gallons of blood does it pump? (Estimate that the heart pumps 50 cm of blood with each beat.)

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