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QUESTION 2 An above-ground circular swimming pool (diameter = 9 m) is initially filled to a height of 1.2 m with water at ambient temperature (20 °C). To drain the pool a short length (2 m) of flexible hose (internal diameter = 4 cm; roughness=0.024 cm) with a ball valve (K = 0.05 for fully open) is located right at the bottom as shown in the figure. Your friend (who did not take fluid mechanics) suggests you let the pool drain by gravity through the short length of hose. You strongly disagree with this approach and instead decide to install a pump that has a long length of the same flexible hose on the pump outlet to direct the water into a storm drain. <<2m 9 m 1.2 m a. Write the general form of the Bernoulli equation in 'head' units for ANY two reference points that include a pump between them. b. Choosing reference points 1 and 2 to be the level of water in the swimming pool and the outlet from the long flexible hose respectively, write the simplified form of the Bernoulli equation. c. Calculate the required exit velocity at point 2 to drain half of the water in the pool in 4 hours. d. What is the longest length of hose that can be installed on the pump outlet given the following: The amount of head added to the fluid by the pump is 4 m Must satisfy the exit velocity criteria from part c) for when the tank is initially full to the 1.2 m height, NOTE: Your answer from part c) should be a value between 1 and 5 m/s. If you did not get a value in this range, then use an exit velocity of 2.5 m/s to solve for the hose length.

QUESTION 2 An above-ground circular swimming pool (diameter = 9 m) is initially filled to a height of 1.2 m with water at ambient temperature (20 °C). To drain the pool a short length (2 m) of flexible hose (internal diameter = 4 cm; roughness=0.024 cm) with a ball valve (K = 0.05 for fully open) is located right at the bottom as shown in the figure. Your friend (who did not take fluid mechanics) suggests you let the pool drain by gravity through the short length of hose. You strongly disagree with this approach and instead decide to install a pump that has a long length of the same flexible hose on the pump outlet to direct the water into a storm drain. <<2m 9 m 1.2 m a. Write the general form of the Bernoulli equation in 'head' units for ANY two reference points that include a pump between them. b. Choosing reference points 1 and 2 to be the level of water in the swimming pool and the outlet from the long flexible hose respectively, write the simplified form of the Bernoulli equation. c. Calculate the required exit velocity at point 2 to drain half of the water in the pool in 4 hours. d. What is the longest length of hose that can be installed on the pump outlet given the following: The amount of head added to the fluid by the pump is 4 m Must satisfy the exit velocity criteria from part c) for when the tank is initially full to the 1.2 m height, NOTE: Your answer from part c) should be a value between 1 and 5 m/s. If you did not get a value in this range, then use an exit velocity of 2.5 m/s to solve for the hose length.

Physics for Scientists and Engineers
Physics for Scientists and Engineers
10th Edition
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter18: Temperature
Section: Chapter Questions
Problem 40AP: A vertical cylinder of cross-sectional area A is fitted with a tight-fitting, frictionless piston of...
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QUESTION 2 An above-ground circular swimming pool (diameter = 9 m) is initially filled to a height of 1.2 m with water at ambient temperature (20 °C). To drain the pool a short length (2 m) of flexible hose (internal diameter = 4 cm; roughness = 0.024 cm) with a ball valve (K = 0.05 for fully open) is located right at the bottom as shown in the figure. Your friend (who did not take fluid mechanics) suggests you let the pool drain by gravity through the short length of hose. You strongly disagree with this approach and instead decide to install a pump that has a long length of the same flexible hose on the pump outlet to direct the water into a storm drain. ←2m 9 m ↑ 1.2 m a. Write the general form of the Bernoulli equation in 'head' units for ANY two reference points that include a pump between them. b. Choosing reference points 1 and 2 to be the level of water in the swimming pool and the outlet from the long flexible hose respectively, write the simplified form of the Bernoulli equation. c. Calculate the required exit velocity at point 2 to drain half of the water in the pool in 4 hours. d. What is the longest length of hose that can be installed on the pump outlet given the following: The amount of head added to the fluid by the pump is 4 m Must satisfy the exit velocity criteria from part c) for when the tank is initially full to the 1.2 m height, NOTE: Your answer from part c) should be a value between 1 and 5 m/s. If you did not get a value in this range, then use an exit velocity of 2.5 m/s to solve for the hose length.
Transcribed Image Text:QUESTION 2 An above-ground circular swimming pool (diameter = 9 m) is initially filled to a height of 1.2 m with water at ambient temperature (20 °C). To drain the pool a short length (2 m) of flexible hose (internal diameter = 4 cm; roughness = 0.024 cm) with a ball valve (K = 0.05 for fully open) is located right at the bottom as shown in the figure. Your friend (who did not take fluid mechanics) suggests you let the pool drain by gravity through the short length of hose. You strongly disagree with this approach and instead decide to install a pump that has a long length of the same flexible hose on the pump outlet to direct the water into a storm drain. ←2m 9 m ↑ 1.2 m a. Write the general form of the Bernoulli equation in 'head' units for ANY two reference points that include a pump between them. b. Choosing reference points 1 and 2 to be the level of water in the swimming pool and the outlet from the long flexible hose respectively, write the simplified form of the Bernoulli equation. c. Calculate the required exit velocity at point 2 to drain half of the water in the pool in 4 hours. d. What is the longest length of hose that can be installed on the pump outlet given the following: The amount of head added to the fluid by the pump is 4 m Must satisfy the exit velocity criteria from part c) for when the tank is initially full to the 1.2 m height, NOTE: Your answer from part c) should be a value between 1 and 5 m/s. If you did not get a value in this range, then use an exit velocity of 2.5 m/s to solve for the hose length.
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