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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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question 3c
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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