If water (p=998 kg/m", u = 10-3 Pa. s) flows through a 50 mm-diameter pipe at 2 m/s, determine the velocity of carbon tetrachloride (p=1590 kg/mº, u=0.958 x 10-Pa. s) flowing through a 60 mm-diameter pipe so that they both have the same dynamic characteristics (Reynolds number similarity, RepUD/).

the velocity of carbon tetra chloride is 1.002 m/s

Explanation:

Given data

water density ρ = 998 kg/m

water viscosity μ = 10³ Pa-s

pipe diameter D = 50 mm = 0.05 m

velocity of carbon v = 2 m/s

tetra chloride density ρ = 1590 kg/m

tetra chloride viscosity μ = 0.958 x 10³ Pa-s

pipe diameter D = 60 mm = 0.06 m

to find out

the velocity of carbon tetra chloride

solution

we know here both of these are of same dynamic characteristics

so we say that

Reynolds number of water is equal to Reynolds number of tetra chloride

ρ (w) * V (w) * D (w) / μ (w) = ρ (ccl4) * V (ccl4) * D (ccl4) / μ (ccl4)

put here all value we get V (ccl4)

V (ccl4) = 998 * 2 * 50 * 0.958 / (1590 * 60)

V (ccl4) = 1.002

the velocity of carbon tetra chloride is 1.002 m/s