A pipeline 0.3 m in diameter divides at a Y into two branches 200 mm and 150 mm in diameter. If the flow rate in the main line is 0 3 m3 s and the mean velocity in the 200-mm pipe is 2 5 m s, determine the flow rate in the 150-mm pipe.

he flow rate in the 150-mm pipe is 0.2215 m³/s

Explanation:

To calculate the flow rate in the pipe, we make use of continuity equation, which is expressed as;

0 = α/αt  cv_∫ pd∀ +  cs_∫pv . dA

now for steady flow rate there is no change with time

so the continuity equation becomes

0 =  cs_∫pv . dA

where p is fluid density, v is fluid velocity and A is area of pipe.

determine the continuity equation   for the system

pV₁A₁ = pV₂A₂ + pV₃A₃

V₁A₁ = V₂A₂ + V₃A₃

Q₁ = V₂A₂ + Q₃

we know that the area is πD²/4

Q₁ = V₂(πD₂²/4) + Q₃

now Q₁ is the flow rate in the main branch( 0.3 m³/s) , Q₃ is the flow rate in 150 mm, V₂ is the velocity in 200 m pipe( 2.5 m/s ), and D₂ is diameter of the branch( 0.2 m )

so we substitute

0.3 = 2.5 (π(0.2)²/4) + Q₃

0.3 = 0.07853 + Q₃

Q₃ = 0.3 - 0.07853

Q₃ = 0.2215 m³/s

therefore the flow rate in the 150-mm pipe is 0.2215 m³/s

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