An averaging tube assembly () is placed vertically in a 3\' - 4\" square duct, a

Question

An averaging tube assembly () is placed vertically in a 3' - 4" square duct, as shown below. The is oriented perpendicular to the flow through the duct, and has holes on t to measure pressure. The holes on the outer pipe are placed in the 3 and 9 o'clock position to measure the static pressure (P_s), while the inner pipe has a hole in the 6 o'clock position (in- flow) to measure the total pressure (rho_T). The differential pressure in the is given by delta P = K(rho/2) bar v^2 is the resistance factor, rho is the air density, and bar v is the average air velocity in the duct. Show how to get the If the differential pressure transmitter indicates a pressure difference of 3.28 [in H_2O], determine the flow rate in the duct (Q) in cfm. Single-phase fluid(air) approximately steady, incompressible flow (Mach number

Explanation / Answer

pitot tube measures velocity of flow by bringing fluid to stagnation state isentropically

P+(1/2)*density*v2+density*g*h=c bernaulli equation

P is static pr

(1/2)*density*v2 is dynamic pressure

in the flow through hole 6 fluid flow is brought to stagnation so dynamic presssure converts to static pressure.

delta P(shown by differential ppressure transmittor)= P+(1/2)*density*v2-P

= (1/2)*density*v2

delta P=3.28*density of water*g=(1/2)*density of air*v2

v=sqrt(3.28*2*density of water*g/density of air)

Q(flow rate in the duct)= Area of duct * average velocity

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