Question

Exhaust gas from a power plant passes through a 15- by 20-ft rectangular duct at an average velocity of 50ft/s. The total length of duct is 250 ft, and there are two 90^o bends. The gas is at 180^oF and about 1 atm, and the properties are similar to those of air. Calculate the pressure drop in the duct and the power required to overcome pressure losses.

Answer 1

let the dimensions of rectangle be a*b

a = 15 ft =4.572 m

b= 20 ft = 6.096 m

hydraulic diameter = (2*a*b)/(a+b) = (2*4.572*6.096)/(4.572+6.096) = 5.225 m

Velocity = v = 15.24 m/s

Reynolds number

Proeperties of exhaust gas are same as that of air

density = 1.29 Kg/m3

Vsicosity = 1.81*10^-5 Pa-s

Subsituting the values to obtain reynolds number

Friction factor

Fr = 0.046*Re^-0.2 = 0.046*(5.67*10⁶)^-0.2 = 0.002

Calculation of Frictional head loss

Now Losses due to 90 ^oC bends

K (for 90 degree bends) = 1

Total losses = 23.70667 +1.3829 =25.08957 m

Power required = Flow rate * density * g * Total head loss = (4.572*6.096)*15.25*1.29*9.81*25.08957 =134950.022 W = 134.95 KW