FLUID MECHANICS We can approximate a car exhaust as 14ft of

FLUID MECHANICS

We can approximate a car exhaust as 14ft of 0.125 ft diameter cast iron pipe. This pipe has six 90° flanged elbows and a muffler. The muffler has a loss coefficient of 8.5. When the exhaust has a flow rate is 0.10 ft3/sec and a temperature of 250°F, what is the pressure at the beginning of the exhaust system?
The exhaust has the same properties as air.

Solution

For flanged elbow, loss coeff = 0.3

For cast iron pipe, roughness e = 0.01 inches

Relative roughness = e/D = 0.01 / (0.125*12) = 0.0067

Area A = 3.14/4 * 0.125^2 = 0.01226 ft^2

Velocity V = Q/A

V = 0.1 / 0.01226

V = 8.153 ft/s

Reynolds number Re = VD / neu

For air at 250 F, we have kinematic viscosity neu = 2.73*10^-4 ft^2/s, density rho = 0.055 lb/ft^3

Re = 8.153*0.125 / 2.73E-4

Re = 3733

From Moody chart at Re = 3733 and rel roughness = 0.0067, we get friction factor f = 0.046

Head loss = [fL/D + K + 6*0.3] * V^2 / (2g)

= [0.046*14/0.125 + 8.5 + 6*0.3] * 8.153^2 / (2*32.2)

= 15.95 ft

Gage Pressure at beginning of exhaust system = rho*15.95 = 0.055*15.95 = 0.879 lb/ft^2 = 0.879/12^2 lb/in^2 = 0.0061 psi