Question

PL 4.53 pss 4 1y2 40 ALL PIrI 70apm K WATER G4T0 YA LVE 20 ft 2o to Tec RON TEE Branch PD=100psi AT INLET OF TEE leo fp Pレ To (mdb Les4AT 16 THE FLOW FROM

Answer 1

Ans) Given,

1.5" Sch 40 pipes

Darcy friction factor = 0.02

Length of pipe from P1 to P2 = 810 ft or 246.89 m

We know, diameter of 1.5" sch 40 pipe = 1.61 " or 0.0409 m

Apply Bernoulli equation between point 1 and 2,

P₁/$\dpi{100} \rho$g + V₁²/2g + Z1 = P₂/$\dpi{100} \rho$g +V₂²/2g + Z2 + H_f + H_m

where, H_f = headloss due to friction

= f L V²/ 2gD

H_m = minor loss

Let point 1 be datum , the, Z1 = 0 and Z2 = 10 ft or 3.05 m

Since pipes are in series , V1 = V2 ,

=> P₁/$\dpi{100} \rho$g = P₂/$\dpi{100} \rho$g + Z2 + H_f + H_m

=> (100 x 6894.76) / (1000 x 9.81) = (44.53 x 6894.76) / (1000 x 9.81) + 3.05 + H_f + H_m ( 1 psi = 6894.76 N /m²)

=> 70.28 = 31.29 + 3.05 + H_f + H_m

=> H_f + H_m = 35.932

=> f L V² / 2gD + (K1 + K2 + K3) V² / 2g = 35.932

=>  f L V² /D + (20 f + 60 f + 9f)V² = 35.932 x 2 x 9.81

=> V² ( f L /D + 89 f) = 705

=> V² [0.02 x 246.89 / 0.0409 + 89(0.02)] = 705

=> 122.5 V² = 705

=> V = 2.4 m/s or 7.87 ft/s

Therefore, we know, Q = A x V

= ($\dpi{100} \pi$/4)(1.61/ 12)² x 7.87

= 0.1112 ft³/s

or 49.91 gpm

Hence, flow from point 1 to 2 is 49.91 gpm