# Fluid Dynamics and its Applications

Lead Author(s): **Openstax Content**

Source: **OpenStax**

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This pack examines flow rate, Bernoulli's Equation and its applications, viscosity and laminar flow, turbulence onset, and more.

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**1. **What is the average flow rate in $cm^3$ /s of gasoline to the engine of a car traveling at 100 km/h if it averages 10.0 km/L? (answer in $cm^3$/s)

**3. **Blood is pumped from the heart at a rate of 5.0 L/min into the aorta (of radius 1.0 cm). Determine the speed of blood through the aorta. (answer in cm/s)

**8. **The human circulation system has approximately 1×10$^{9}$ capillary vessels. Each vessel has a diameter of about 8 *µ*m . Assuming cardiac output is 5 L/min, determine the average velocity of blood flow through each capillary vessel. (answer in cm/s)

**12. **The main uptake air duct of a forced air gas heater is 0.300 m in diameter. What is the average speed of air in the duct if it carries a volume equal to that of the house's interior every 15 min? The inside volume of the house is equivalent to a rectangular solid 13.0 m wide by 20.0 m long by 2.75 m high. (answer in m/s)

**19. **If the pressure reading of your pitot tube is 15.0 mm Hg at a speed of 200 km/h, what will it be at 700 km/h at the same altitude? (answer in mm Hg)

**21. **Every few years, winds in Boulder, Colorado, attain sustained speeds of 45.0 m/s (about 100 mi/h) when the jet stream descends during early spring. Approximately what is the force due to the Bernoulli effect on a roof having an area of 220 $m^2$? Typical air density in Boulder is 1.14 kg/$m^3$, and the corresponding atmospheric pressure is 8.89×10$^4$ $N/m^2$ . (Bernoulli's principle as stated in the text assumes laminar flow. Using the principle here produces only an approximate result, because there is significant turbulence.) (answer in ×10$^5$ N)

**27. **The left ventricle of a resting adult's heart pumps blood at a flow rate of 83.0 $cm^3$ /s , increasing its pressure by 110 mm Hg, its speed from zero to 30.0 cm/s, and its height by 5.00 cm. (All numbers are averaged over the entire heartbeat.) Calculate the total power output of the left ventricle. Note that most of the power is used to increase blood pressure. (answer in W)

**30. **What force is needed to pull one microscope slide over another at a speed of 1.00 cm/s, if there is a 0.500-mm-thick layer of 20º C water between them and the contact area is 8.00 $cm^2$ ? (answer in ×10$^{-5}$ N)

**31. **A glucose solution being administered with an IV has a flow rate of 4.00 $cm^3$ /min . What will the new flow rate be if the glucose is replaced by whole blood having the same density but a viscosity 2.50 times that of the glucose? All other factors remain constant. (answer in cm$^3$/min)

**33. **A small artery has a length of 1.1×10$^{-3}$ m and a radius of 2.5×10$^{-5}$ m . If the pressure drop across the artery is 1.3 kPa, what is the flow rate through the artery? (Assume that the temperature is 37º C.) (answer in ×10$^{-2}$ mm$^{3}$/s)

**39. **Using the equation of the previous problem, find the viscosity of motor oil in which a steel ball of radius 0.8 mm falls with a terminal speed of 4.32 cm/s. The densities of the ball and the oil are 7.86 and 0.88 g/mL, respectively. (answer in mPa ∙ s)

**60. **Assuming that blood is an ideal fluid, calculate the critical flow rate at which turbulence is a certainty in the aorta. Take the diameter of the aorta to be 2.50 cm. (Turbulence will actually occur at lower average flow rates, because blood is not an ideal fluid. Furthermore, since blood flow pulses, turbulence may occur during only the high-velocity part of each heartbeat.) (answer in ×10$^{-4}$ $m^3/s$)

**62. **You can smell perfume very shortly after opening the bottle. To show that it is not reaching your nose by diffusion, calculate the average distance a perfume molecule moves in one second in air, given its diffusion constant *D* to be 1.00×10$^{-6}$ $m^2$ /s . (answer in ×10$^{-3}$ m)

**64. **Oxygen reaches the veinless cornea of the eye by diffusing through its tear layer, which is 0.500-mm thick. How long does it take the average oxygen molecule to do this? (answer in ×10$^{2}$ s)

**66. **Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography. (answer in s)

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