7. A pipe with a series of holes as shown in the figure is used in many engineer

Question

7. A pipe with a series of holes as shown in the figure is used in many engineering systems to distribute gas into a system. The volume flow rate through each hole depends on the pressure difference across the hole and is given by 0.67Ao (24P) 1/2 where Ao is the area of the hole, P is the pressure difference across the hole, and is the density of the gas in the pipe. If the pipe is sufficiently large, the pressure will be uniform along the pipe. A distribution pipe for air at 20 is 0.5 meters in diameter and 8 m long. The gage pressure in the pipe is 100 Pa. The pressure outside the pipe is atmospheric at 1 bar. The hole diameter is 2.5 cm, and there are 40 holes per meter length of pipe. The pressure is constant in the pipe. Find the velocity of the air entering the pipe. 8 m Problem 7 Problem 6

Explanation / Answer

given guage pressure dP = 100 Pa
diameter, d = 0.5 m
length, l = 8 m
hole diameter, d' = 2.5 cm

now, volume flow rate through each hole = Q = 0.067*pi*(d')^2(2*dP/rho)^0.5 /4
Q = 0.067*pi*(0.025)^2(2*100/1.225)^0.5 / 4 = 4.20234*10^-4 m^3/s
so net volume flow rate out of 40 holes = 40Q = 0.0168 m^3/s

tshi can be considered inlet volume flow rate = pi*d^2*v/4
pi*0.5^2*v/4 = 0.0168
v = 0.0856094 m/s

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