Oil flows from tank A through 500 ft of 6 in new asphalt dip

Oil flows from tank A through 500 ft of 6 in new asphalt dipped cast iron pipe to point B at elevation 100.0 in the following figure. What pressure in psi will be needed at A to cause 0.450 cubic feet per sec (cfs) of oil to flow. (sp gr =0.840 and viscosity = 2.27x10^-5 sq ft per second e=0.0004 and f = 0.0235.

Solution

The problem is one of frictional flow through a pipe against a gravitational head.

The lost head is given by the formula:   f* (L/d)*V^2/(2g), where f = friction factor =.0235

d = diameter of pipe - 0.5 ft

L = 500 ft length of pipe
V = velocity which can be found from flow and diameter as

V =Q/A (Q being the volumetric flow), V = 0.45/A = 2.2918 fps

The loss of head due to friction is f*(L/d)* (V*V/(2g))= 1.917 ft

The Reynolds number computed from the given viscosity and the velocity is Vd/(viscosity) = 54000 approx laminar

SO one may use the laminar flow expression for flow in a pipe under a pressure gradient

V = dP ** d^2/(32* L * viscosity), where viscosity = kin. viscosity*density

Pressure diff dP= 32* mu*L*V/(d^2) = 32*(.84*62.2)*2.27* (10-5)*500*2.292/(.5*.5)

Giving approx 2.8 *62.2 * (32.2 = g) pounds/sft

Appprox 39 psi is reqd if no frictional head loss

The frictional head loss of 1.917 ft can be converted to pressure and added to this figure, giving approx

1.92*.84*62.2/144 psi or .7 psi

So a total of 40 psi may be required to push the fluid up the pipe. Additionally the head of 20 ft from 80 to 100 ft is to be added, so this figure of 1.92 needs to be modified to 21.92, giving a new figure of 21,92/1.92 *.7 or 8 psi

Total 39+8 =47 psi

Round off to 50 psi to take careof other losses.