3. Drinking water is piped from a water main into a house via a PVC (e, smooth) pipe. There is a total of 20 linear feet of 1" diameter pipe between the water main and a point just inside house that is 10ft above the water main. This drinking water pipe branches from the water main (K₁ = 0.2), a water meter taps into the pipe (K = 7), there are two 90° bends (K = 1.5), and finally a (fully open) water shutoff ball valve (K = 0.05) before the point just inside the house. The pipe maintains a flow of 0.05 ft/s. If the goal is for the gage pressure of the water to be 8640 lb/ft? (aka 60 psi) just inside the house, what must the gage pressure of the water be at the water main? Leave your answer in lb/ft² water meter 90° elbow water shutoff house branch flow 2-10 ft ball valve, fully open 2-0 ft-water main 90 elbow "drawing not to scale
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1.correct equation: (ΔP / (ρg)) + ΔZ = f * (L / D) * (v^2 / 2g) + (v^2 / 2g) * ΣK_L
2.v = Q / A = 9.17 ft/s
3. Reynolds number: Re = (v * L) / ν = (v * L) / (ρ * μ) = 63,154
4.The pipe is smooth so: ε_d = 0
5.Friction factor from the Moody diagram: f = 0.020
6.Pressure difference: ΔP = P₁ - P₂ = P₁ - 8640 lb_f
7.Head loss due to elevation difference: ΔZ = Z₁ - Z₂ = -10 ft
8.Summation of pipe fittings and losses: ΣK_L = 0.2 + 7 + 2(1.5) + 0.05 = 10.25
9.values to plug in
- Length of the pipe: L = 20 ft
- Diameter of the pipe: D = 1/12 ft
- Fluid density: ρ = 1.94 slugs/ft³
- Gravitational acceleration: g = 32.2 ft/s²
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