Assume that the inlet pipe is connected to a closed reservoi

Assume that the inlet pipe is connected to a closed reservoir/tank with liquid level at ground level (0 ft).

All pipes are Schedule 40 seamless steel. The 4-in inlet pipe is 10 ft long. Branch 1 is 2-in, Branch 2 is 4-in, both have a total length of 20 ft. The 4-in exit pipe is also 10 ft long.

For water at 70oF, vary the pressure at the source from 2 psig to 6 psig with 2 psi increments, and determine the flow rate in gpm through the Branch 1 and Branch 2, and at discharge location. summarize results from all cases (2, 4, 6 psig at supply) in a table.

D, 2.00 in Branch 1 K 5 for open valve K 10 for open valve Branch 2 D, 4.00 in Plan view

Solution

Given:

P_A= 2 psig = 16.2 psi

P_{bracnh 1, 2} = 4 psig = 18.7 psi

P_B= 6 psig = 20.7 psi

D_branch1 = 2 inch

D_branch2 = 4 inch

D_A = 4 inch

D_B= 4 inch

K₁ = 5

K₂= 10

L_{1, 2} = 20 ft = 240 inch

L_{A, B} = 10 ft = 120 inch

R₁ = 8 x L₁ x P₁ / (² x D₁⁵ x g)

= 8 x 240 x 18.7/ (2 x 2⁵ x 9.81)

= 5.8

R₂ = 8 x L₂ x P₂ / (² x D₂⁵ x g)

= 8 x 240 x 18.7/ (2 x 4⁵ x 9.81)

= .18

K = Sqrt (R₂ / R₁) = 0.176