Question

1.) Water flows at a rate of 10 gallons per minute in a new horizontal 0.75 in diameter galvanized pipe (E=0.0005 ft). Determine the pressure gradient, Ap/1, along the pipe. (note: 231 in' per gallon)

Answer 1

sol? 9 First, find the velocity from the continuiting explotion : AV = VA V AV А AV 0.02228 ft = 7.36f7 5 T 0² 3.68.103 were where the substituted values for the cross-section area diameter, and the volume flow-rate, converted from the given units, into the standard BG enit system To find the pressure change, set the Bernouli equation between the inlet point (1), and the outlet point (2): eft +Zq the 4 vi P2 + + Z, r 9-8 1 29 Notice that V = V₂ and that the pipe horizontal, meaning cancel out. that the height terms will

Substitute the expression for the head loss by a and frusther Simplify the equation : l v? P, r +2 P2 g +Z+f + D 22 29 P, r 욕 f P2 r D 29 P, P₂ f r D 29 Aph f r ΔΡ. D 29 f pv 4 D Here we observe that the proper value of the friction factor is needed to solve the expression. In order to find the friction factor, we must first calculate the value of the Reynolds numb PVD M 1.938 x 7.262 x 0.75 12 2.344 x 100 0.3752x105. RE 11 11

where the values of water density and dynamic viscocity are taken from the table B.1. From the table 8.1 take the value of the equivalent roughness É for the galvani žed iron pipe, and calculate the friction factor from the formula : 2.51 VE = -2 loq + 3.7 REVE EID 2.5) + -2log If 3.9 RENE f 0.0369 simplified pressure substitute the friction factor into the Bernoulli equation, we obtain for the difference: f pre ДР D 2 l 2 eb 0.0367 1.938 x 7.262 ft3 2 0.75 12 eb 30.01 X ++3 Psi AP 0.21 ft Result.

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