For gases at velocities greater than 200 ft/s, pressure drop is found from the following equation.

where subscripts 1 and 2 represent inlet and outlet conditions, respectively.

Example 4.2 A pitot tube reads 1 in of mercury in a pipe. What is the velocity of air flowing in a pipe at 14.7 psi and 70 °F? Use the following information.

C = 0.98 - 1.00; diameter of pipe, d = 0.335 ft; density of mercury = 846.7 lb/ft³

Density of air = 0.075 lb/ft³; specific heat ratio k = 1.4, pressure drop (ΔP) = 70.55 lb_f/ft²

Solution

C Velocity of air, V

Velocity of the gas is greater than 200 ft/s,

Assume adiabatic flow.

C Pressure at the wall, P_o:

Inlet pressure P₁ = 14.696 psi = 2116.2 lb_f/ft²

C Velocity of the air, V (Equation 4.3):