Pitot-Static Gage

Air moves with uniform velocity (section [B]) through a pipe. Some of that air headed directly for the projecting, tube-end of the gage, is decelerated ahead of the tube then comes nearly to rest, momentarily, just ahead of the tube opening, [A]. The event just described is called "stagnation of the flow." The kinetic energy of the flow changes into an increased pressure of the air at the tip of the gage. This pressure difference created is important information.

Δp = p_A,stagnated - p_{B,free-flowing}

At the bottom of the image (right) is an equation that yields the rate of flow of air provided the pressure difference can be determined. The density of the flowing air is ρ = 1.6 kg/m³. Use the hydrostatic principle to obtain the pressure difference. Exercise care when looking at distances. Also, if a mercury level goes down in one leg it goes up the same distance in the other leg. Start at "[A]" and follow a hydrostatic path to "[B]." (Hg means mercury).

Calculate the mass flow rate of air through the pipe.

p_A + ρ_airg_o(600 + 30 + 10)mm ρ_Hgg_o(20)mm - ρ_airg_o(20 + 600)mm = p_B

p_A - p_B = ρ_Hgg_o(20)mm - ρ_airg_o(600 + 30 + 10)mm + ρ_airg_o(20 + 600)mm

p_A - p_B = ρ_Hgg_o(20)mm - ρ_airg_o(20)mm

A last step is:

p_A - p_B = (ρ_Hg - ρ_air)g_o(20)mm

Putting in numbers (approximate for air):

p_A - p_B = (13,600 - 1.6)kg/m³9.81 m/s²(0.02)m = 2,668 Pa

Notice that the density of air is negligible. But don't guess - let the math throw out what is small. Thus the mass flow is:

All calculations are idealized.