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3. You are on a placement in a chemical plant and have been asked to calculate the force on the walls of a circular pipe (radius, R = 0.02 m) using pressure tappings at the two stations (A and B) shown in Figure Q3. The chemical in the pipe has viscosity, μ = 5 x 103 kg / m s, and density, p = 660 kg/m³. The pressure tappings are separated by a distance, L = 20 m, and are connected to a manometer filled with water (p = 1000 kg/m³) with an indication, Ah = 40 mm. a) is the pressure at B higher or lower than the pressure at A? For g = 9.8 m/s², calculate the magnitude of this pressure change. b) The flow in the pipe is laminar and fully developed, so can be assumed to follow a Hagen-Poiseuille distribution: u = 1 др 4μ 8χ (x² - R²) What is the velocity at point 1 in section B, which is located 0.01 m away from the pipe axis? c) What is the maximum velocity across the cross-section at station B? What is the maximum velocity at station A? d) Recall that the critical Reynolds number for transition in pipes occurs at Reynolds numbers based on the diameter in the range Rep = 2300 - 3500. Explain whether our assumption of laminar flow is reasonable. chemical Ah R 0.01 m water Figure Q3: Chemical flow through a pipe

3. You are on a placement in a chemical plant and have been asked to calculate the force on the walls of a circular pipe (radius, R = 0.02 m) using pressure tappings at the two stations (A and B) shown in Figure Q3. The chemical in the pipe has viscosity, μ = 5 x 103 kg / m s, and density, p = 660 kg/m³. The pressure tappings are separated by a distance, L = 20 m, and are connected to a manometer filled with water (p = 1000 kg/m³) with an indication, Ah = 40 mm. a) is the pressure at B higher or lower than the pressure at A? For g = 9.8 m/s², calculate the magnitude of this pressure change. b) The flow in the pipe is laminar and fully developed, so can be assumed to follow a Hagen-Poiseuille distribution: u = 1 др 4μ 8χ (x² - R²) What is the velocity at point 1 in section B, which is located 0.01 m away from the pipe axis? c) What is the maximum velocity across the cross-section at station B? What is the maximum velocity at station A? d) Recall that the critical Reynolds number for transition in pipes occurs at Reynolds numbers based on the diameter in the range Rep = 2300 - 3500. Explain whether our assumption of laminar flow is reasonable. chemical Ah R 0.01 m water Figure Q3: Chemical flow through a pipe

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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3. You are on a placement in a chemical plant and have been asked to calculate the force on the walls of a circular pipe (radius, R = 0.02 m) using pressure tappings at the two stations (A and B) shown in Figure Q3. The chemical in the pipe has viscosity, μ = 5 x 103 kg / m s, and density, p = 660 kg/m³. The pressure tappings are separated by a distance, L = 20 m, and are connected to a manometer filled with water (p = 1000 kg/m³) with an indication, Ah = 40 mm. a) is the pressure at B higher or lower than the pressure at A? For g = 9.8 m/s², calculate the magnitude of this pressure change. b) The flow in the pipe is laminar and fully developed, so can be assumed to follow a Hagen-Poiseuille distribution: u = 1 др 4μ 8χ (x² - R²) What is the velocity at point 1 in section B, which is located 0.01 m away from the pipe axis? c) What is the maximum velocity across the cross-section at station B? What is the maximum velocity at station A? d) Recall that the critical Reynolds number for transition in pipes occurs at Reynolds numbers based on the diameter in the range Rep = 2300 - 3500. Explain whether our assumption of laminar flow is reasonable. chemical Ah R 0.01 m water Figure Q3: Chemical flow through a pipe
Transcribed Image Text:3. You are on a placement in a chemical plant and have been asked to calculate the force on the walls of a circular pipe (radius, R = 0.02 m) using pressure tappings at the two stations (A and B) shown in Figure Q3. The chemical in the pipe has viscosity, μ = 5 x 103 kg / m s, and density, p = 660 kg/m³. The pressure tappings are separated by a distance, L = 20 m, and are connected to a manometer filled with water (p = 1000 kg/m³) with an indication, Ah = 40 mm. a) is the pressure at B higher or lower than the pressure at A? For g = 9.8 m/s², calculate the magnitude of this pressure change. b) The flow in the pipe is laminar and fully developed, so can be assumed to follow a Hagen-Poiseuille distribution: u = 1 др 4μ 8χ (x² - R²) What is the velocity at point 1 in section B, which is located 0.01 m away from the pipe axis? c) What is the maximum velocity across the cross-section at station B? What is the maximum velocity at station A? d) Recall that the critical Reynolds number for transition in pipes occurs at Reynolds numbers based on the diameter in the range Rep = 2300 - 3500. Explain whether our assumption of laminar flow is reasonable. chemical Ah R 0.01 m water Figure Q3: Chemical flow through a pipe
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