In this problem, we're going to do a very simplistic analysis of blood flow in a human body. We will ignore viscosity, so the numbers we get in parts (b) and (c) will be very rough approximations of the actual values. This will still give us some insight into the human circulatory system.

We will use the following numbers, which are typical numbers for an average human:

• the diameter of the aorta is 3.20 cm
• the number of capillaries in the body is 10 billion
• the diameter of a capillary is 1.00 x 10^-5 m
• the length of a capillary is 600 microns, or 6.00 x 10^-4 m

Typically, the human heart pumps blood at the rate of 5-6 liters per minute, but when exercising that rate can be somewhat higher. We'll use a higher value (assuming you are working out), given below. Note that we will also neglect any effects of gravity in this problem.

Note that our simplifying assumptions impact parts (b) and (c) especially. Accounting for the effects of viscosity, the blood would flow significantly more slowly through the capillaries than your answer for (b) would suggest, and thus spend considerably longer in a capillary than you calculate in (c). This long time is important to allow for the exchange of oxygen and carbon dioxide between your cells and your blood, for instance.

Part A: You are doing some moderate exercise and the blood flow through your heart is 7.50 liters/minute. All of that blood flows through your aorta, Calculate the average speed of the blood in the aorta, using the diameter of the aorta given above.
_______ m/s

Part B: Using numbers stated above, and neglecting viscosity, calculate the average speed of the blood in a capillary.
_______ m/s

Part C: Continuing from part (b), how much time does it take a particular red blood cell to flow from one end of a capillary to the other?
_______ s