Consider the fully developed flow of glycerin at 40°C through a 60-m-long, 4-cm-diameter, horizontal, circular pipe. If the flow velocity at the centerline is measured to be 6 m/s, determine the pressure difference across this 60-m-long section of the pipe and the useful pumping power required to maintain this flow. The density and dynamic viscosity of glycerin at 40°C are rho = 1252 kg/m3 and µ = 0.3073 kg/m·s, respectively.

The pressure difference across the 60 m long section of the pipe is 1106.28 kPa

The pumping power required to maintain the flow is 4.171 kW

Explanation:

For a fully developed laminar flow in a pipe we have

Plugging in the values gives

= 6·(1-2500·r²)

The average velocity =

= 3 m/s

= = v(πD²/4) = 3 m/s(π·(0.04 m)²/4) =3.7699× 10⁻³ m³/s

Reynolds' number is given by;

Re = 488.903

Since Re < 2300 we have a laminar flow

f = 0.131

Head loss

The energy equation is given by

Where, V₁ =V₂, and z₁ = z₂

, Therefore

P₁ - P₂ = ΔP = ρg() =1252×9.81×90.07 = 1106280.796 Pa = 1106.28 kPa

The power;

.

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