12.4 Viscosity and Laminar Flow; Poiseuille’s Law

(a) Calculate the retarding force due to the viscosity of the air layer between a cart and a level air track given the following information—air temperature is $\text{20}º\text{ C}$, the cart is moving at 0.400 m/s, its surface area is $2 . \text{50} \times \text{10}^{−2} \text{m}^{2}$, and the thickness of the air layer is $6.00 \times \text{10}^{- 5} \text{m}$. (b) What is the ratio of this force to the weight of the 0.300-kg cart?

A glucose solution being administered with an IV has a flow rate of $4 . \text{00} \text{cm}^{3} /\text{min}$. 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.

A small artery has a length of $1 . 1 \times \text{10}^{- 3} \text{m}$ and a radius of $2.5 \times \text{10}^{- 5} \text{m}$. If the pressure drop across the artery is 1.3 kPa, what is the flow rate through the artery? (Assume that the temperature is $\text{37}º\text{ C }$.)

The arterioles (small arteries) leading to an organ, constrict in order to decrease flow to the organ. To shut down an organ, blood flow is reduced naturally to 1.00% of its original value. By what factor did the radii of the arterioles constrict? Penguins do this when they stand on ice to reduce the blood flow to their feet.

(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?

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.

A layer of oil 1.50 mm thick is placed between two microscope slides. Researchers find that a force of $5 . \text{50} \times \text{10}^{- 4} \text{N}$ is required to glide one over the other at a speed of 1.00 cm/s when their contact area is $6 . \text{00} \text{cm}^{2}$. What is the oil’s viscosity? What type of oil might it be?

the example dealt with the flow of saline solution in an IV system. (a) Verify that a pressure of $1 . \text{62} \times \text{10}^{4} \text{N}/\text{m}^{2}$ is created at a depth of 1.61 m in a saline solution, assuming its density to be that of sea water. (b) Calculate the new flow rate if the height of the saline solution is decreased to 1.50 m. (c) At what height would the direction of flow be reversed? (This reversal can be a problem when patients s…

During a marathon race, a runner’s blood flow increases to 10.0 times her resting rate. Her blood’s viscosity has dropped to 95.0% of its normal value, and the blood pressure difference across the circulatory system has increased by 50.0%. By what factor has the average radii of her blood vessels increased?

An oil gusher shoots crude oil 25.0 m into the air through a pipe with a 0.100-m diameter. Neglecting air resistance but not the resistance of the pipe, and assuming laminar flow, calculate the gauge pressure at the entrance of the 50.0-m-long vertical pipe. Take the density of the oil to be $\text{900} \text{kg}/\text{m}^{3}$ and its viscosity to be $1 . \text{00} \left(\right. \text{N}/\text{m}^{2} \left.\right) \cdot \text{s}$ (or $1.00 \text{Pa } \cdot \text{s }$). Note that you must take into account the pressure due to the 50.0-m co…