## Q. 7.Q.15

What is the pressure in a 9.7-in bore horizontal pipe, if the bore of the pipe narrows to 4.1 in downstream where the pressure is 65 psig and 28,200 gal of fluid per hour with a specific gravity (SG) of 0.87 is flowing? Neglect losses.

## Verified Solution

$A_{2}=\frac{3.14\times 4.1\times 4.1}{4\times 12\times 12} \ ft^{2}=0.092\$ft²

$A_{1}=\frac{3.14\times 9.7\times 9.7}{4\times 12\times 12} \ ft^{2}=0.51$ft²

$V_{2}=\frac{28,200\times 0.1337}{60\times 60\times 0.092} \ ft/s=11.38$ft/s

$V_{1}=\frac{11.38\times 0.092}{0.51} \ ft/s=2.05$ft/s

$\frac{p_{1}}{\gamma}+\frac{V_{1}^{2}}{2g}+Z_{1}=\frac{p_{2}}{\gamma}+\frac{V_{2}^{2}}{2g}+Z_{2}$

$\frac{p_{1}}{62.4}+\frac{2.05\times 2.05}{2\times 32.2}+0=\frac{(65+14.7)144}{62.4}+\frac{11.38\times 11.38}{2\times 32.2}+$0

$p_{1} = (183.92 + 2.01 − 0.065)62.4 = 11,597.97 \ psfa = 80.54 \ psia = 65.84 \ psig$