The estimated total pressure loss for the duct including the contraction and expansion is 60.7 Pa.
The circular metal duct 20 ft (6 m) in length with an abrupt contraction at the inlet and an abrupt expansion at the exit. Both the contraction and expansion have an area ratio of 0.6. The duct has a diameter of 10 in. (25 cm) and a flow rate of 600 cfm (0.28 m3/s).
The total pressure loss for the duct including the contraction and expansion can be estimated using the following equation:
ΔP = (K_c + K_e)ρv^2/2
where:
ΔP is the total pressure loss in Pa
K_c is the minor loss coefficient for the contraction
K_e is the minor loss coefficient for the expansion
ρ is the density of the fluid in kg/m3
v is the velocity of the fluid in m/s
The minor loss coefficients for the contraction and expansion can be found from tables or by using the following equations:
K_c = 0.5(1 - A_r)^2
K_e = 0.5(1 - A_r)^2
where A_r is the area ratio of the contraction or expansion.
In this case, the area ratio is 0.6, so the minor loss coefficients are:
K_c = 0.5(1 - 0.6)^2 = 0.14
K_e = 0.5(1 - 0.6)^2 = 0.14
The density of air at room temperature is approximately 1.225 kg/m3.
The velocity of the fluid in the duct can be calculated using the following equation:
v = Q/A
where:
Q is the flow rate in m3/s
A is the cross-sectional area of the duct in m2
The cross-sectional area of the duct is:
A = πd^2/4
where d is the diameter of the duct in m.
Substituting the known values into the equation for the velocity, we get:
v = 600 cfm * (0.028317 m3/ft3) / (π * (0.254 m/12 in.)^2 / 4) = 17.2 m/s
Now we can calculate the total pressure loss for the duct:
ΔP = (K_c + K_e)ρv^2/2 = (0.14 + 0.14)(1.225 kg/m3)(17.2 m/s)^2/2 = 60.7 Pa