Question

Water with density of p=1.94 slug/ft3 and dynamic viscosity of 2.34X10-5 slug/ft.s flows from the basement to the second floor through the 0.75 in (0.0625 ft)-diameter copper pipe (a drawn tubing wit e=0.000005 ft) at a rate of Q=12.0 gal/min=0.0267 ft3/s and exits through a faucet of diameter 0.50 in. as shown in the figure

Answer 1

Please refer the following images for the solution.

Given: X155 3= 1:94 slug life? - 1.94% 32.174 = 62.42 lbm/ft? 44 2:34, 16% slug/AS = 2.34 x17x ** 32.174 = 75.29.4bftis d = 0-75 18 = 0.0625 ft es 0.000005 Ft Q- 12.0 gal/min = 0.0257 ft/s de=0.850 in 0.04 167 ft + 2, + v,² where, P2 V = Q 0.0277 Solution Applying Bernoulli's equation at D and Ⓡ, neglecting losses P, P₂ +22+ sg 2g sg 2g - O Amospheric pressure head (gauge) (Assurning caturm head) 8.7 ft/s Id² *0.06252 2₂= 10+10=20 ft V2 = 0.0267 19.58 ft/s Ix de 2X0.04167 Above equation reduces to Pi 2,2 sg 2g zg Piz, + V2 V3 38 2g Pi 62.42x32.2 Z₂ + V₂² + 20+ (19-58-8.7) 2x 32.2 P, = 49801.373 lbf / f12 (gauge) P- 49801.373+2116.22 = 5 1917.593 lb/ft? (absolute

2 Applying at ① and ② comsidering Bernoullis equation major losses only Pi + 2 + V 2 P2 sg Z + V2 the sg 2g 2g where he fLv, ² agd Calculation of friction factor of 45080.18993 Reynolds number of the flow Re=3xd 62.42 x 8.78 0.0625 75.296155 Relative roughness of the pipe, 0.000005 -8x16 d d 0.0625 Using moodys diogaon for @ - 8ko and Re - 45080-16993 friction factor of the 0.02165 pipe, + Above equation reduces to - 2 + 2 fl ve sg 28 2g agd Pi 20+ (19.584-8.72) (0.02165x60x8.73) 62.42x32.2 2x32. 2x0.0625 2 ₂ 32:2 :./P, = 98899. 10 lbt/ft2 (gauge) 1. P = 98899.10 + 2116.22 :.P-101015:32 164/ft? (Absolute)

c) The total minor losses in the pipe. hm EK L x V2 [{1x1.5) +10 ] + V, 2 + (2x V 22 ) 28 hm = ((4x 1.5)4 (10)]x 8.72 2 x 19.582 2x32.2 + 2x32.2 hm = 30.71 ft 1. Pressure loss due to minor losses Permine) - sghm - 62.4232.2 *30.7| ... Pec minor) - 61724.77 lbr/ft? Pressure at (1) will be P 98899.10+6 1724.77 P4-160623.87 ebr/ft2 (gauge) Pi =160623.877 2116.22 IP, = 162740.09 lbr/ft² Absolute (range)