Question

How to use Bernoulli equation to derive air mass flow? Please give me a more detailed process, thank you very much
example:

tange * HTC2C155 2 pipe wall jave t r easure flow speed - decreases Tut de pressure or limites flow rate n orifice plate Few @EVA , van fit fege. Att 1 Pi-p= 2 I (Vok mys & A V2 = A prop (volume flow rate). ੨ Pvr ( 4 ) (-ਨਾ ਆ oh=fgh Water

Answer 1

Bernoulli's Equation for Air mass flow rate :- Q pipe ③ outlet. Inlet → Air Ain dy Z1 & Consider ais blow thowugh the above buipe through two dibberent section as shown in the above figure of air. Let the inter condition A be, and outlet condition Py = Pressure at section B = Pressure at section V1 = Velocity at Section 1 V2 = velocity at section ® Air. Sg - density at section 0 P2 = Density at secten > datum Z1 = datum available at sechino 22 - Density at Section © Air. Now let. 23 apply the Bernoulli's equation P + 2 P V, ² +Z1 = P2 + 2/2 2 2 ² 2 - 0 since the pipe is placed horizontal so, 21 = 22 : Pet 2 Piv,2 = Pzt 1 2 1 2 V22 Now let us assume that di >> da so Viao Plto = P2 + 1/2 P2 V2 ² 16 V ² = P1-P2 21P1-P2) V2 = J Pa *tery important point here we have to notice that density of the ain at section and section will be different Because air is compressible.

V2 from equation © we should So, while calculating velocity take the value of ß not Pj (because P17 P2) Since we know the velocity at section © and also the area So, from continuity equation. Q- ALVI = A2 V2 we can write, = Az JAP - PB) a = 1 a ² J? (P2-B) mes. And also mass blow rate, ma 8Q m = $. da PM in = I di JPB (P1-P2) or if AP = PI-B the mass flow rate in = 7 d Jah AP J - ma

Now to find AP. P B. 72222 Air -- - manometric fluid. manometer is used as So, to find P P2 =AP, let us say a of the two columns. above then thene will be height difference having manometric fluid fluid density. Let us say manometric Pm = so AP = P1 P2 - Img h Now substituting the value of sp in equation 3 we get, So, the mass flow rate of air, in a I de J2 (8m Gh). P or in = A2 S2 (8mgh). Pa

Note :- Bernoulli's equation can be applied for air flow. Brel there is an exception we should keep in mind that It holds good d only when th only when the density changes are very low at section and l ie As should be small. * As we know, Bernoullis equation relates to the pressure changes to velocity changes in the flow of buid For small Change in velaituries (ie at section D and ) density does not change much (from section to ③.). But if the velocity of air is very say above 0.3 Mach Number there is ben considerable error occurs the fluid Because when flows at the veroury more than through a region faster advect 0.3 Mach then fluid might than the effects of its pressure. # equation So, Bernoulli's applicable only for air at wwer speeds.

Note: If volume flow rate Q is in m3/s, velocity V is in m/s, datum in m and density is in kg/m3 then mass flow rate will be in kg/s.