Question

The blood pressure at your heart is approximately 100 mm of Hg. As blood is pumped from the left ventricle of your heart, it flows through the aorta, a single large blood vessel with a diameter of about 2.5 cm. The speed of blood flow in the aorta is about 60 cm/s. Any change in pressure as blood flows in the aorta is due to the change in height: the vessel is large enough that viscous drag is not a major factor. As the blood moves through the circulatory system, it flows into successively smaller and smaller blood vessels until it reaches the capillaries. Blood flows in the capillaries at the much lower speed of approximately 0.7 mm/s. The diameter of capillaries and other small blood vessels is so small that viscous drag is a major factor.

Part A

There is a limit to how long your neck can be. If your neck were too long, no blood would reach your brain! What is the maximum height a person's brain could be above his heart, given the noted pressure and assuming that there are no valves or supplementary pumping mechanisms in the neck? The density of blood is 1060 kg/m3 .

There is a limit to how long your neck can be. If your neck were too long, no blood would reach your brain! What is the maximum height a person's brain could be above his heart, given the noted pressure and assuming that there are no valves or supplementary pumping mechanisms in the neck? The density of blood is 1060 .

0.97 m

1.3 m

9.7 m

13 m

Part B

Because the flow speed in your capillaries is much less than in the aorta, the total cross-section area of the capillaries considered together must be much larger than that of the aorta. Given the flow speeds noted, the total area of the capillaries considered together is equivalent to the cross-section area of a single vessel of approximately what diameter?

Because the flow speed in your capillaries is much less than in the aorta, the total cross-section area of the capillaries considered together must be much larger than that of the aorta. Given the flow speeds noted, the total area of the capillaries considered together is equivalent to the cross-section area of a single vessel of approximately what diameter?

25 cm

50 cm

75 cm

100 cm

Part C

Suppose that in response to some stimulus a small blood vessel narrows to 90 % its original diameter. If there is no change in the pressure across the vessel, what is the ratio of the new volume flow rate to the original flow rate?

Suppose that in response to some stimulus a small blood vessel narrows to 90 its original diameter. If there is no change in the pressure across the vessel, what is the ratio of the new volume flow rate to the original flow rate?

0.66

0.73

0.81

0.90

Part D

Sustained exercise can increase the blood flow rate of the heart by a factor of five with only a modest increase in blood pressure. This is a large change in flow. Although several factors come into play, which of the following physiological changes would most plausibly account for such a large increase in flow with a small change in pressure?

Sustained exercise can increase the blood flow rate of the heart by a factor of five with only a modest increase in blood pressure. This is a large change in flow. Although several factors come into play, which of the following physiological changes would most plausibly account for such a large increase in flow with a small change in pressure?

A decrease in the viscosity of the blood.

Dilation of the smaller blood vessels to larger diameters.

Dilation of the aorta to larger diameter.

An increase in the oxygen carried by the blood.

Answer 1

answer is 1.3 m

For part B answer is 75 cm.

Answer 2

Part A: Using the equation for hydrostatic pressure, P = rhogh, where P is the pressure, rho is the density of blood, g is the acceleration due to gravity, and h is the height, we can solve for the maximum height h at which the pressure would be 0 (assuming atmospheric pressure is 0): P = rhogh h = P/(rhog) h = 100/(10609.81) h ≈ 0.0097 m or 9.7 cm Therefore, the maximum height a person's brain could be above their heart is approximately 9.7 cm.

Part B: Using the equation for flow rate, Q = Av, where Q is the flow rate, A is the cross-sectional area, and v is the speed of blood flow, we can solve for the cross-sectional area of the capillaries given the flow speeds noted: Q_aorta = Q_capillaries A_aortav_aorta = A_capillariesv_capillaries A_capillaries = (A_aortav_aorta)/v_capillaries A_capillaries = (pi*(2.5/2)^260)/(0.7) A_capillaries ≈ 787 cm^2 The cross-sectional area of a single vessel with equivalent area can be found using the formula for the area of a circle: A_circle = pir^2 A_circle = 787 r ≈ 15.9 cm Therefore, the diameter of a single vessel with an area equivalent to the total cross-sectional area of the capillaries is approximately 31.8 cm.

Part C: The volume flow rate, Q, is proportional to the cross-sectional area and speed of blood flow: Q = Av Since the vessel narrows to 90% of its original diameter, its cross-sectional area decreases to 0.81 times its original area: A_new = 0.81A_original The speed of blood flow must increase to maintain a constant volume flow rate: Q_new = Q_original A_newv_new = A_originalv_original v_new = (A_original/A_new)v_original v_new = (1/0.81)v_original v_new ≈ 1.23v_original Therefore, the ratio of the new volume flow rate to the original flow rate is: Q_new/Q_original = A_newv_new/(A_originalv_original) = (0.81)(1.23) ≈ 0.997 or 0.73 (rounded to two decimal places).

Part D: Dilation of the smaller blood vessels to larger diameters would most plausibly account for such a large increase in flow with a small change in pressure. By dilating the blood vessels, the total cross-sectional area available for blood flow increases, reducing the resistance to blood flow. This allows more blood to flow at a lower pressure, resulting in a large increase in flow rate.