Chapter 9 Viscous fluid flow (Chap. 14 in the textbook page 341)

1. Chapter 9Viscous fluid flow(Chap. 14 in the textbook page 341) Dr. Haykel Abdelhamid Elabidi April/May 2014/Ju T 1435

2. Units of Chapter 9 • Viscosity • Flow in the circulatory system

3. Viscosity • The viscosity of a fluid is a measure of its resistance to flow under an applied force. • The greater the viscosity, the larger the force required to maintain the flow, and the more energy that is dissipated. • Honey has a high viscosity, water a smaller viscosity, and air a still smaller viscosity.

4. Viscosity • Viscosity is readily defined by considering a simple experiment: • The below figure shows two flat plates separated by a thin fluid layer. Figure 1 • The lower plate is held fixed, a force is required to move the upper plate at a constant speed. • This force is needed to overcome the viscous forces due to the liquid and is greater for a highly viscous fluid Moving plate Fixed plate

5. Viscosity

6. Viscosity • As the temperature increases viscosity decreases, for liquids. • As the temperature increases viscosity increases, for gases. • Because viscous forces are usually small, fluids are often used as lubricants to reduce friction.

7. Viscosity The force required is: This is a very small force and is consistent with the observation that an air track is nearly frictionless

8. Flow in The Circulatory System The blood • The circulatory system transports the substances required by the body and takes off the waste products of metabolism. • In order to perform a large number of functions, the blood contains many different constituents, including red blood cells, white blood cells, platelets, and proteins. • - However, for our purposes, it is sufficient to treat the blood as a uniform fluid with viscosity and density:

9. Flow in The Circulatory System The Cardiovascular System • This system includes the heart, and an extensive system of arteries, vascular beds containing capillaries, and veins. • A particularly interesting compound of the cardiovascular system is the arteriovenous anastomosis (AVA), or shunt. • http://medical-dictionary.thefreedictionary.com/arteriovenous+anastomosis • These shunts are particularly important, since the surrounding muscle tissue can adjust the diameter of the blood flow to various organs as conditions change. • Smaller shunts in the skin are open if the body needs to release heat or to increase skin temperature.

10. Flow Resistance

11. Flow in The Circulatory System Example 14.5. page 348: The aorta of an average adult human has a radius 1.3 x 10-2m. What are the resistance and the pressure drop over a 0.2-m distance, assuming a flow rate of 10-4 m3s-1?

12. Flow in The Circulatory System The pressure drop over the 0.2-m distance is then: • This is very small value of the pressure drop, compared to the total pressure drop in the system, which is about 13.3 kPa. • Most of the flow resistance and pressure drops occur in the smaller arteries and vascular beds of the body (Table 14.4 p349).

13. Flow in The Circulatory System

14. Flow in The Circulatory System

15. Flow in The Circulatory System With =2.084x10-3 Pa s, the resistance of one capillary is: Solution Example 14.6. page 349: There are N= 4.73x107 capillaries in parallel, so there effective resistance is :

16. Flow in The Circulatory System Some approximate flow rates and resistances for the resting, reclining adult.

17. Flow in The Circulatory System • Suppose we know the resistances of N sections, each of which leads into the next. • The total pressure drop is as follows • Each pressure drop is the total flow rate Q times the resistance of that section. • The effective flow resistance Rs of these sections which are said to be in series, is the sum of the resistances.

18. Homeworks: Exercises 14.3; 14.23; 14.39 Thank you for your attention See you next time Inchallah