. A pipeline is to be built to carry 300,000 lbm/hr of air over a distance of 90

Question

. A pipeline is to be built to carry 300,000 lbm/hr of air over a distance of 900 ft. A compressor will steadily supply air at this flow rate, and at 100 psia, 80 deg F inlet stagnation conditions. The exit static pressure must be greater than or equal to 20 psia, according to system requirements. The Cole-King Pipe Company can supply the necessary pipe, in diameters ranging from 10" - 24", in 2" increments. Select the smallest pipe which will deliver the required mass flow rate at the stated co Assume isothermal flow, and average friction factor= 0.015. Calculate the exit Mach number and pressure for the selected pipe size. Ans. 12 in., 0.38, 48.7 psia.

Explanation / Answer

For isothermal compressible flow in constant cross-section pipe with constant friction factor f, we have

fL/D = (P12 - P22) rho1 / (P1*G2) + ln (P2/P1)2.....where rho represents density

From air properties at P1 = 100 psia and T1 = 80 deg F, we have rho1 = 0.501 lb/ft3

0.015*900 / D = (1002 - 202)*122 * 32.2 * 0.501 / (100*G2) + ln (20 / 100)2

13.5 / D = 223011.5 / G2 - 3.2188

Now G = rho*u.......where u is the velocity

13.5 / D = 223011.5 / (0.501*u)2 - 3.2188

13.5 / D = 888488.5 / u2 - 3.2188...........eqn1

Mass flow rate m = rho*A*u...where A is cross-section area = pi/4 D2....where D is the dia of the pipe

300000 / (60*60) = 0.501 * 3.14 / 4 * D2 * u

D2 * u = 211.89...........eqn2

Solving eqn1 and eqn2, we get D = 0.965 ft = 11.58" and u1 = 227.2 ft/s

Hence, closest pipe dia available = 12''

Area A = 3.14 / 4 * (12/12)2 = 0.785 ft2

u1 = m / (rho1*A)

= 300000 / (60*60) / (0.501 * 0.785)

= 211.89 ft/s

G = rho1*u1

= 0.501 * 211.89

G = 106.1

0.015*900 / 1 = (1002 - P22)*122 * 32.2 * 0.501 / (100*106.12) + ln (P2 / 100)2

Solving this, P2 = 48.7 psia

From air properties, at 48.7 psia and 80 deg F, we get rho2 = 0.244 lb/ft3 and sound speed = 1140 ft/s

u2 = G/rho2

= 106.1 / 0.244

u2 = 434.8 ft/s

Mach number = 434.8 / 1140 = 0.38

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