phy240 hw8

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Question 1
Blood flows through the aorta at speed 40 cm/s. The cross-sectional area of the aorta is initially
4 cm2. Though a single capillary is very small, the total cross-sectional area of all the capillaries
fed by the aorta is 6000 cm2, over half a square meter! What is the flow rate of blood through
the capillaries?
Question 2
A 100 m tall water tower holds a huge amount of water, so that the water level in the tower
remains approximately constant even when some water flows out through a faucet at the bottom
of the tower. With what speed does water come out the faucet when opened? What is the flow
rate of water out of the faucet, volume of water per time, if the faucet has radius 1 cm?
Question 3 (optional)
A pump is designed to pump water at a flow rate of 3 gallons per second at zero elevation. The
water flows into a very long hose (of constant cross-section) that can withstand large pressures.
You walk the end of the hose uphill and notice that the flow rate decreases. You continue
walking uphill until the flow rate drops to zero. To what elevation have you walked, and what is
the pressure at the pump? (Hint: the pump is supplying the same energy per volume to the water,
but now that energy is going into maintaining a pressure difference at the pump, rather than to
accelerating the water.) You use this pump to pump water up 1000 ft. What is the flow rate
through the end of the hose at this elevation?
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