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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 = pA,stagnated - pB,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.
pA + ρairgo(600 + 30 + 10)mm ρHggo(20)mm - ρairgo(20 + 600)mm = pB
pA - pB = ρHggo(20)mm - ρairgo(600 + 30 + 10)mm + ρairgo(20 + 600)mm
pA - pB = ρHggo(20)mm - ρairgo(20)mm
A last step is:
pA - pB = (ρHg - ρair)go(20)mm
Putting in numbers (approximate for air):
pA - pB = (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.