Question

Problem 1. Water flows from a large tank through a smooth pipe of length 80 m. Both the tank free surface and jet exit are exposed to the atmosphere. Take the density of water p = 1000 kg/m3, dynamic viscosity of water u = 0.001 kg/m.s, atmospheric pressure = 100 kPa, and gravity = 9.8 m/s2. Calculate the volumetric flow rate through the pipe. Neglect entrance losses to the pipe. Hint: Consider the inlet and outlet sections of the pipe as Sections (1) and (2). [10 points] 10 m Pipe Diameter, D = 180 mm Outflow at Patm 80 m

Answer 1

K 1 10m - 0'18 m m² DATUM -80 m an of Head Given Data : Z₂ = 10 m/(Height at Patry section (1) from Datum) o (section (2) is on the Datum). batma 100 kpa 2100 KN) y out flow at patm. Swater = 1000 kg/m² To determine ; volumenic flow rate; l water = 0.001 Kylmsee (Q2 = A₂ U2) through the pipe. g = 9.8 m/s2 where; A2 = A 2 = ( x[048)2] m2. Uz - Velocity of water the pipe (m/see). calculation Losses : 1) Ening loss at section (1) = 0 ☺ Exit loss section (2) - (u3/28) aii) frictional Head loss, hy = 0 (3 Darcy Friction factor, f=0 because the bike is SMOOTH). total head loss= h = (U27/29) Applying Bernoullis eqr at Sections & ②; we haver $2° V22 V22 Rg Zla 2g zg Zy10 V₂² 3) V2= 9.8X10) = 98 >> V2-98 g or; U₂ = 7N2 m/sec) Thues; Q=( x[0-98)*712) = 0.2519414 m3/sec. Hence; The volumetic flow rate through the pipe is Q2 letres (see) at O (A 4,270 + + + 72 + + ₂2 + 0.251911 coumeest OY 251.91