1. The purpose of this and next problem is to calculate and compare pressure drops under various situations to get a feel for the magnitudes of pressure drops due to viscous dissipation, constrictions, and height changes. Comparing problem 1 and 2 will give you a feel for differences between gases and liquids. Oil with 300 cp viscosity and 0.85 g/cm density is flowing in a pipe that is 4 ft in diameter at a rate of 10 m/min. These parameters are those typical of the Alaskan oil pipeline. (a) What does Bernouilli's equation predict for pressure drop for a completely horizontal 1 mile section of this pipe? (b) What does the Hagen-Poiseuille equation predict for pressure drop for a completely horizontal 1 mile section of this pipe? (c) Why is there a difference in the answers for a and b. Which is correct? At some point along this pipe there is a sudden change (a constriction) in the diameter of the pipe from 4 ft to 2 ft without changing the height of the pipes centerline. (d) What does Bernouilli's equation predict for pressure drop between a point 100 ft before this pipe and 100 ft after this pipe? (e) What does Hagen-Poiseuille equation predict for pressure drop between a point 100 ft before this pipe and 100 ft after this pipe? (f) Why is there a difference in the answers for d and e? Which is correct? At some point along this 4 ft diameter pipe there is a 100 ft high hill. (g) What does Bernouilli's equation predict for pressure drop between the bottom and top of this hill? (h) What does Hagen-Poiseuille equation predict for pressure drop between the bottom and top of this hill? Is there a difference between the answers in (g) and (h)? Why or why not? (j) What did you learn by doing the above problems? Make a list of things you learned. 1. The purpose of this and next problem is to calculate and compare pressure drops under various situations to get a feel for the magnitudes of pressure drops due to viscous dissipation, constrictions, and height changes. Comparing problem 1 and 2 will give you a feel for differences between gases and liquids. Oil with 300 cp viscosity and 0.85 g/cm density is flowing in a pipe that is 4 ft in diameter at a rate of 10 m/min. These parameters are those typical of the Alaskan oil pipeline. (a) What does Bernouilli's equation predict for pressure drop for a completely horizontal 1 mile section of this pipe? (b) What does the Hagen-Poiseuille equation predict for pressure drop for a completely horizontal 1 mile section of this pipe? (c) Why is there a difference in the answers for a and b. Which is correct? At some point along this pipe there is a sudden change (a constriction) in the diameter of the pipe from 4 ft to 2 ft without changing the height of the pipes centerline. (d) What does Bernouilli's equation predict for pressure drop between a point 100 ft before this pipe and 100 ft after this pipe? (e) What does Hagen-Poiseuille equation predict for pressure drop between a point 100 ft before this pipe and 100 ft after this pipe? (f) Why is there a difference in the answers for d and e? Which is correct? At some point along this 4 ft diameter pipe there is a 100 ft high hill. (g) What does Bernouilli's equation predict for pressure drop between the bottom and top of this hill? (h) What does Hagen-Poiseuille equation predict for pressure drop between the bottom and top of this hill? Is there a difference between the answers in (g) and (h)? Why or why not? (j) What did you learn by doing the above problems? Make a list of things you learned
