الرحيم الرحمن الله بسمBiofluids , BME. 396

Assignment 1

1. For the Poiseuille flow and Newtonian fluid of viscosity in a tube of radius R, a. Show that the wall shearing stress can be obtained from the relationship:

b. What is the value of the flow rate in a 5-mm-diameter vessel that causes a wall shear stress of 0.84 N/m2? Would the corresponding flow be laminar or turbulent?

2. A liquid (viscosity =0.004 Ns/m2; density =1050 kg/m3) is pumped through the circular tube, as shown in Figure below. A differential manometer is connected to the tube, as shown, to measure the pressure drop along the tube

a. When the differential reading h is 7 mm, what is the mean velocity in the tube?b. When the liquid is pumped through the circular tube, as shown in the figure, what is the

height h, when the Reynolds number is equal to 1000?

3. A saline solution (density=1050 kg/m3) is ejected from a 20-mm-diameter syringe, through a 2-mm-diameter needle, at a steady velocity of 0.5 m/s.

a. Estimate the pressure developed in the syringe. Neglect viscous effects.b. Estimate the value of velocity at which the saline solution would be turbulent in the 2-mm-

diameter needle. At that velocity, what is the pressure developed in the syringe?

4. A schematic of a 100-cm-long catheter having an inside diameter of 0.4 mm connected to a syringe is shown in the figure below. In a typical infusion pump, the plunger is driven at a constant velocity, as illustrated. For a velocity of 50 mm/min, what volume rate of flow will discharge through the catheter, and what pressure will develop in the syringe? Neglect entrance effects, and assume the fluid to have a viscosity of 0.002 Ns/m2 and a density of 1000 kg/m3.

5. Quick questions on Alveolar Ventilation:a. Determine the total lung capacity of a patient with vital capacity of 4.6 L, functional

residual capacity of 2.6 L, and residual volume of 1.3 L.b. Determine the expiratory reserve capacity of a patient with functional residual capacity of

2.9 L and a residual volume of 1.3 L.c. Find the vital capacity for a person with a total lung capacity of 7 L and a residual volume

of 1.5 L.d. Find the inspiratory reserve volume for a patient with a total lung capacity of 7 L, a

functional residual capacity of 2.7 L, and a tidal volume of 500 mL.

6. Find the rate of breathing in breaths per minute for a patient with a tidal volume of 500 mL, a cardiac output of 5 L/min, and a ventilation/perfusion ratio of 1.1.

7. A person has a breathing rate of 18 breaths per minute with a tidal volume of 400 mL, a heart rate of 100 bpm, and a stroke volume of 90 mL. What is this person’s ventilation to perfusion ratio?

8. From the static pressure-volume diagram shown belowa. Find the average compliance of the lung, in m5/N, during tidal breathing for the patient.b. Calculate the work of breathing, in Joules, for a single breath for a patientc. If the person is taking 12 breaths per minute, what is the power expended by breathing?

The cross-hatched area is 1.91 L.cm H2O.

9. The figure below shows a volume-time curve for a patient with chronic obstructive pulmonary disease (COPD). Find the forced expiratory flow rate, FEF25–75%, for this patient. Assume the residual volume, RV, to be 0.5 L.

10. A given person has 15 g Hgb per 100 mL blood and a partial pressure of alveolar CO2 of 33 mmHg. Based on the hemoglobin saturation curve shown below, how much hemoglobin a comparable person would need to have the same amount of oxygen in his/her blood at 14,000 ft above mean sea level. Assume the person at the higher altitude has a partial pressure of alveolar carbon dioxide of 15 mmHg.

11. Whole blood (assume =0.004 Ns/m2) is placed in a concentric cylinder viscometer. The gap width is 1 mm and the inner cylinder radius is 30 mm. Estimate the torque exerted on the 10-cm-long inner cylinder. Assume the angular velocity of the outer cylinder to be 30 rad/min.

12. Whole blood is forced from a large reservoir through a small rigid tube (diameter = 2 mm; length=500 mm) and discharges into the atmosphere. If the gauge pressure in the reservoir is 4 x104 N/m2, estimate the discharge from the tube in m3/s. The blood hematocrit is 55 percent and the blood temperature is 30oC. Assume the relative viscosity of plasma to be 1.24 x 10–3 Ns/m2.

13. Using the Einstein equation to predict viscosity as a function of hematocrit and temperature, calculate the viscosity of blood at 37 oC using a hematocrit of 50 and a plasma viscosity of 1.24 x10–3 Ns/m2.

14. A patient with thalassemia trait has a blood test that shows a hematocrit of 40 percent and a red blood cell concentration of 5.5 x106 RBC/mm3.

a. Determine the mean corpuscular volume for this patient.b. If the patient has a measured hemoglobin of 10 g/100 mL, calculate the mean corpuscular

hemoglobin and the mean corpuscular hemoglobin concentration.

15. Calculate the ratio of metabolic compensation to respiratory compensation for a person with a bicarbonate concentration of 24 meq/L and a PCO2 of 25 mmHg. Does this person have acidosis or alkalosis? Respiratory or metabolic?

16. Blood is forced from a large reservoir through a small rigid tube (diameter=2 mm, length =500 mm) and discharges into the atmosphere. If the gauge pressure in the reservoir is 2 x104 N/m2, estimate the discharge from the tube in m3/s. Given:

a. blood hematocrit =45 percent b. blood temperature =37 oC c. viscosity of plasma =0.00125 Ns/m2 d. blood density =1060 kg/m3

17. The arterial compliance of a vessel is 3.0=1010 m2/Pa; the artery diameter is 5 mm; the wall thickness is 0.2 mm. Estimate the modulus of elasticity.

18. The modulus of elasticity of a vessel is 2.0 MPa; the artery diameter is 5 mm; the wall thickness is 0.2 mm.

a. Estimate the compliance.b. For this vessel, what increase in pressure, in mmHg, would be required to increase the

vessel radius by 10 percent?

19. In the figure below, a tube with modulus of elasticity of 1 MPa is anchored between two stationary ports and injected with a volume of water. The wall thickness of the tube is 1 mm. Estimate the vessel compliance and the volume of water required to raise the pressure by 6 kPa.

20. Carotid artery modulus of elasticity is reported as 3.12 x105 N/m2 and 4.18 x105 N/m2 in carotid arterial atherosclerosis, compared to a value of 2.34 x105 N/m2 in the control group. Estimate the pulse wave velocity.

21. The diameter of the carotid artery might change from 6.3 to 7.1 mm from diastole to systole. Find the difference in pulse wave velocity predicted by this change in diameter.

Good Luck for all