Question

A fluid flows through two horizontal pipes of equal length which are connected together to form a pipe of length 2l. The flow is laminar and fully developed. The pressure drop for the first pipe is 1.789 times greater than it is for the second pipe. If the diameter of the first pipe is D, determine the diameter of the second pipe.

Answer 1

Answer:

Explanation:

For rate of flow of liquid in a pipe , the formula is

Q = π p r⁴ / 8 η l

where Q is volume of liquid flowing per unit time , p is pressure drop across pipe , r is radius of pipe , η is coefficient of viscosity and l is length of pipe

If η and l are constant for two pipes having equal rate of flow as in the given case

p₁ r₁⁴ = p₂ r₂⁴

p₁ = 1.789 p₂ ( given )

r₁ = D/2

1.789 p₂ x (D/2)⁴ = p₂ x r₂⁴

r₂ = $\frac{D}{2}\times\sqrt[4 ]{1.789}$

2 x r₂ = D  x 1.1565

D₂ =  D  x 1.1565