A fluid of viscosity 0.7 ns/m2 and specific gravity 1.3 is flowing through a circular pipe of diameter 100mm. The maximum shear stress at the pipe wall is given as 196.2 n/m2, find. I) the pressure gradient. Ii) the average velocity and iii) reynolds number of the flow.
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Dear student,
# Answer-
(1) Pressure gradiant dp/dx = -7848 N/m^2 per m
(2) Average velocity v = 3.5 m/s
(3) Reynolds number Re = 650
# Given-
μ = 0.7 N.s/m^2
ρ = 1300 kg/m^3
D = 100mm = 0.1m
R = 50mm = 0.05 m
τ = 196.2 N/m^2
# Step-by-step solution-
(1) Pressure gradiant
τ = -dp/dx × R/2
196.2 = -dp/dx × 0.05/2
dp/dx = -7848 N/m^2 per m
(2) Average velocity
v = -vmax/2
v = -1/8μ ×(dp/dx)×R^2
v = -1/(8×0.7) ×(-7848) × (0.05)^2
v = 3.5 m/s
(3) Reynolds number
Re = ρ×v×D/μ
Re = 1300×3.5×0.1/0.7
Re = 650
Hope you understand well.
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