Suppose the flow rate of blood in a coronary artery has been reduced to half its normal value by plaque deposits. By what factor has the radius of the artery been reduced, assuming no turbulence occurs. Hint: The heart tries to maintain constant pressure difference across arteries in both cases. Think and Prepare 1. What is the relationship between the flow rate Q and the radius of an artery for a given length, pressure gradient and viscosity? r plaque no plaque =

Suppose the flow rate of blood in a coronary artery has been reduced to half its normal value by plaque deposits. By what factor has the radius of the artery been reduced, assuming no turbulence occurs. Hint: The heart tries to maintain constant pressure difference across arteries in both cases. Think and Prepare 1. What is the relationship between the flow rate Q and the radius of an artery for a given length, pressure gradient and viscosity? r plaque no plaque =

College Physics

1st Edition

ISBN:9781938168000

Author:Paul Peter Urone, Roger Hinrichs

Publisher:Paul Peter Urone, Roger Hinrichs

Chapter12: Fluid Dynamics And Its Biological And Medical Applications

Section: Chapter Questions

Problem 37PE: (a) Suppose a blood vessel's radius is decreased to 90.0% of its original value by plaque deposits...

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(a) Suppose a blood vessel's radius is decreased to 90.0% of its original value by plaque deposits and the body compensates by increasing the pressure difference along the vessel to keep the flow rate constant. By what factor must the pressure difference increase? (b) If turbulence is created by the obstruction, what additional effect would it have on the flow rate?
(a) As blood passes through the capillary bed in an organ, the capillaries join to form venules (small veins). If the blood speed increases by a factor of 4.00 and the total cross-sectional area of the venules is 10.0 cm2, what is the total cross-sectional area of the capillaries feeding these venules? (b) How many capillaries are involved if their average diameter is 10.0 m?
(a) Using Bernoulli's equation, show that be measured fluid speed v for a pitot tube, like the one in figure 14.32(b), is given by v=( 2gh)1/h , where h is be height of be manometer fluid, p' is the density of the manometer fluid, p is the density of the moving fluid, and g is be acceleration due to gravity. (Note that v is indeed proportional to the square root of h, as stated in text) (b) Calculate v for moving air if a mercury manometer's h is 0.200 m. Figure 14.32 Measurement of fluid speed on Bernoulli’s principle. (a) A manometer is connected to two tubes close together and small enough not to disturb the flow. Tube 1 is open at the end facing the flow. A dead spot having zero speed is created there. Tube 2 has an opening on the side, so the fluid has a speed v across; thus, pressure there drops. The difference in pressure at the manometer is 12v22 , so h is proportional to . 12v22 (b) This type of velocity measuring device is a Prandtl tube, also known as a pitot tube.
Liquid toxic waste with a density of 1752 kg/m3 is flowing through a section of pipe with a radius of 0.312 m at a velocity of 1.64 m/s. a. What is the velocity of the waste after it goes through a constriction and enters a second section of pipe with a radius of 0.222 m? b. If the waste is under a pressure of 850,000 Pa in the first section of pipe, what is the pressure in the second (constricted) section of pipe?
(a) Verify that a 19.0% decrease in laminar flow through a tube is caused by a 5.00% decrease in radius, assuming that all other factors remain constant. (b) What increase in flow is obtained from a 5.00% increase in radius, again assuming all other factors remain constant?
(a) Verify that a 19.0% decrease in laminar flow through a tube is caused by a 5.00% decrease in radius, assuming that all other factors remain constant, as stated in the text. (b) What increase in flow is obtained from a 5.00% increase in radius, again assuming all other factors remain constant?
(a) Using Bernoulli's equation, show that the measured fluid speed v for a pitot tube, like the one in Figure 12.7(b), is given by v=( 2gh)1/2 , where h is the height of the manometer fluid, is the density of the manometer fluid, is the density of the moving fluid, and g is the acceleration due to gravity. (Note that v is indeed proportional to the square root of h, as stated in the text.) (b) Calculate v for moving air if a mercury manometer's h is 0.200 m. Figure 12.7 Measurement of fluid speed based on Bernoulli's principle. (a) A manometer is connected to two that are close together and small enough not to disturb the flow. Tube 1 is open at the end facing the flow. A dead spot having zero speed is created there. Tube 2 has an opening on the side, and so the fluid has a speed V across the opening; thus, pressure there drops. The difference in pressure at the manometer is 12v22 , and so h is proportional to 12v22 . (b) This type of velocity measuring device is a Prandtl tube, also known as a pitot tube.
(a) What is the pressure drop due to the Bernoulli effect as water goes into a 3.00-cm-diameter nozzle from a 9.00-cm-diameter fire hose while carrying a flow of 40.0 L/S? (b) To what maximum height above the nozzle can this water rise? (The actual height will be significantly smaller due to air resistance.)
(a) Calculate the absolute pressure at an ocean depth of 1 000 m. Assume the density of seawater is 1 030 kg/m3 and the air above exerts a pressure of 101.3 kPa. (b) At this depth, what is the buoyant force on a spherical submarine having a diameter of 5.00 m?
The pressure drop along a length of artery is 100 Pa, the radius is 10 mm, and the flow is laminar. The average speed of the blood is 15 mm/s. (a) What is the net force on the blood in this section of artery? (b) What is the power expended maintaining the flow?
If the pressure in the esophagus is -2.00 mm Hg while that in the stomach is +20.0 mm Hg, to what height could stomach fluid rise in the esophagus, assuming a density of 1.10 g/mL? (This movement will not occur if the muscle closing the lower end of the esophagus is working properly.)
Pressure in the spinal fluid is measured as shown in Figure 11.43. If the pressure in the spinal fluid is 10.0 mm Hg: (a) What is the reading of the water manometer in cm water? (b) What is the reading if the person sits up, placing the top of the fluid 60 cm above the tap? The fluid density is 1.05 g/mL. Figure 11.43 A water manometer used to measure pressure in the spinal fluid. The height of the fluid in the manometer is measured relative to the spinal column, and the manometer is open to the atmosphere. The measured pressure will be considerably greater if the person sits up.