Question

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.

Answer 1

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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