Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr.

Size: px

Start display at page:

Download "Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr."

Georgiana McCoy
5 years ago
Views:

1 Middle East Technical University Department of Mechanical Engineering ME 305 Fluid Mechanics I Fall 2018 Section 4 (Dr. Sert) Study Set 3 Reading Assignments You can find the answers of some of the following questions in your textbook. For others you need to go to other references. R1. Study the derivation of the Bernoulli equation in the handout available at the course web site. If you want, you can study read it in your textbook too. R2. Read about Daniel Bernoulli at R3. What is a sluice gate? Read about it in your textbook and learn how the Bernoulli Equation is applied to it. R4. In our lectures we talked about the Venturi meter as a flow rate measurement device. Two variants of it are known as nozzle meter and orifice meter. Read about them in your textbook. 1. Provide 1 or 2 sentence definitions of the following terms pressure head, velocity head, elevation head, total head, piezometric head static pressure, dynamic pressure, stagnation pressure, total pressure vena contracta energy line, hydraulic grade line orifice meter, nozzle meter, Venturi meter 2. Consider a flow in the horizontal plane where elevation changes are negligible. How does the pressure change across curved streamlines? What about straight streamlines? 3. a) How do we measure static pressure? b) How do we measure stagnation pressure? 4. Draw a schematic of Prandtl s tube and explain its working principle. 5. (Munson) A person holds her hand out of an open car window while the car drives through still air at 100 km/h. Under standard atmospheric conditions, what is the maximum pressure on her hand? What would be the maximum pressure if the car were an Indy 500 racer traveling at 350 km/h? 1

6. (Munson) What s the relation between V A and V B. 7. (Munson) Determine the flowrate through the pipe. 8.

For example, a typical prairie dog burrow contains two entrances - a flat front door and a mounded back door.

the mound. Assume the air velocity across the back door is 1.07V 0.

2 6. (Munson) What s the relation between V A and V B. 7. (Munson) Determine the flowrate through the pipe. 8. (Munson) Some animals have learned to take advantage of the Bernoulli effect without having read a fluid mechanics book. For example, a typical prairie dog burrow contains two entrances - a flat front door and a mounded back door. When the wind blows with velocity V 0 across the front door, the average velocity across the back door is greater than V 0 because of the mound. Assume the air velocity across the back door is 1.07V 0. For a wind velocity of 6 m/s, what pressure difference, p 1 p 2, is generated to provide a fresh airflow within the burrow? 9. (Munson) Water flows steadily in the shown vertical variable-area pipe. Determine the flowrate if the pressure in each of the gages reads 50 kpa. 2

10. (Munson) Air flows through the device shown. If the flowrate is large enough, the pressure within the constriction will be low enough to draw the water up into the tube.

3 10. (Munson) Air flows through the device shown. If the flowrate is large enough, the pressure within the constriction will be low enough to draw the water up into the tube. Determine the flowrate and the pressure needed at section (1) to draw the water into section (2). 11. (Munson) An air cushion vehicle is supported by forcing air into the chamber created by a skirt around the periphery of the vehicle. The air escapes through the 7.5 cm clearance between the lower end of the skirt and the ground. The vehicle has a mass of 4500 kg and its shape is a 10 m by 20 m rectangle. The volume of the chamber is large enough so that the kinetic energy of the air within the chamber is negligible. a) Determine the flowrate, Q, needed to support the vehicle. b) If the ground clearance were reduced to 5 cm, what flowrate would be needed? c) If the vehicle mass is reduced to 2500 kg and the ground clearance maintained at 7.5 cm, what flowrate would be needed? Hint: Assume the pressure inside the chamber to be uniform and write a Bernoulli equation between a point inside the chamber with negligible speed and high pressure (this pressure will support the weight of the vehicle) and the exit point with low pressure and high speed. 12. (Munson) Air is drawn into a wind tunnel used for testing automobiles as shown. a) Determine the manometer reading, h, when the velocity in the test section is 100 km/h. Note that there is a 2.5 cm column of oil of specific gravity 0.9 on the water in the manometer. b) Determine the difference between the stagnation pressure on the front of the automobile and the pressure in the test section. Hint: Try to make use of 3 points on the same streamline, first one before the entrance with negligible speed and atmospheric pressure, second one inside the tunnel, and the third one on the car. 3

4 13. (Munson) Air is drawn into a small wind tunnel. Atmospheric pressure is 100 kpa and the temperature is 25 o C. Neglecting the viscous effects, a) determine the pressure at the stagnation point on the nose of the airplane. Hint: For the BE, consider a point before the entrance with negligible speed and atmospheric pressure, b) determine the manometer reading, h, for the manometer attached to the static pressure tap within the test section of the wind tunnel where the air velocity is 50 m/s, c) should we be worried about compressibility effects? Hint: For the BE consider the first point to be the one described in the previous hint, and the second one to be a point in the test section with the given speed. 14. Show the energy line and the hydraulic grade line of the following flow. Consider zero gage pressure at the free surface and at the exit. If we attach piezometers and pitot tubes to sections 1 and 2, what will be the liquid levels in them? 1 2 z 4

15. (Munson) A small card is placed on top of a spool as shown. It is not possible to blow the card off the spool by blowing air through the hole in the center of the spool.

5 15. (Munson) A small card is placed on top of a spool as shown. It is not possible to blow the card off the spool by blowing air through the hole in the center of the spool. The harder one blows, the harder the card sticks to the spool. In fact, by blowing hard enough it is possible to keep the card against the spool with the spool turned upside down (Note: It may be necessary to use a thumb tack to prevent the card from sliding from the spool). Explain this phenomenon. 16. (Munson) Observations show that it is not possible to blow the table tennis ball from the funnel shown in Fig. (a). In fact, the ball can be kept in an inverted funnel (Fig. (b)) by blowing through it. The harder one blows through the funnel, the harder the ball is held within the funnel. Explain this phenomenon. Here is an explanation: 5

Write important assumptions used in derivation of Bernoulli s equation. Apart from an airplane wing, give an example based on Bernoulli s principle

Write important assumptions used in derivation of Bernoulli s equation. Apart from an airplane wing, give an example based on Bernoulli s principle HW#3 Sum07 #1. Answer in 4 to 5 lines in the space provided for each question: (a) A tank partially filled with water has a balloon well below the free surface and anchored to the bottom by a string. The