Example Problem – Matching a Pump to a Piping System Given: Water (ρ= 1000 kg/m3, µ= 1.00 ×10-3kg/m⋅s) is pumped from one large reservoir to another large reservoir that is at a higher elevation. The free surfaces of both reservoirs are exposed to atmospheric pressure, as sketched. The dimensions and minor loss coefficients are provided in the figure. The pipe is 2.2 cm I.D. cast iron pipe. The total pipe length is 150.0 m. The entrance and exit are sharp. There are three regular threaded 90-degree elbows, and one fully open threaded globe valve. The pump’s performance (supply curve) is approximated by the expression 2availablepump, u supply0HhH==−±aVwhere shutoff head H0= 20.0 m of water column, coefficient a= 0.072 m/Lpm2, available pump head Havailableis in units of meters of water column, and volume flow rate V±is in units of liters per minute (Lpm). Valve z1 Reservoir z2 Pump 1z2– z1V1≈0 Reservoir 2V2≈0 Dz2– z1= 8.0 m (elevation difference) D= 2.2 cm (pipe diameter) KL, Entrance= 0.50 (sharp pipe entrance)
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