Question

Air flows steadily and isentropically from standard atmospheric conditions to a receiver pipe through a converging duct. The cross-sectional area of the throat of the converging duct is 0.05 ft2. Determine the mass flowrate in lbm/s through the duct if the receiver pressure is 10 psia.

Answer 1

The answer is "0.0728"

Step-by-step explanation:

Given value:

`P_0= 14.696\ ps\\\\\ p _(0)= 0.00238 (slue)/(ft^(3))\\\\\ A= 0.05 ft^2\\\\\ T_0= 59^(\circ)f = 518.67R\\\\\ air \ k= 1\\\\ \ cirtical \ pressure ( P^*)=P_0* (2)/(k+1)^{(k)/(k-1)}\\`

`= 14.696* ((2)/(1.4+1))^{(1.4)/(1.4-1)}\\\\=7.763 Psia\\\\`

if
`P<P^(*) \to` flow is chocked

if
`P>P^(*) \to` flow is not chocked

When P= 10 psia <
`P^(*)`
`\to` not chocked

match number:

`\ for \ P= \ 10\ G= \sqrt{(2)/(k-1)[((\ p_(0))/(p))^{(k-1)/(k)}-1]}`

`= \sqrt{(2)/(1.4-1)[((14.696)/(10))^{(1.4-1)/(1.4)}-1]}`

`M_0=7.625`

`p=p_0(1+(k-1)/(2) M_0 r)^(1)/(1-k)`

`=0.00238(1+(1.4-1)/(2)0.7625`)^{(1)/(1-1.4)}\\\\\ p=0.001808 (slug)/(ft^3)`

`\ T= T_0(1+(k-1)/(2) Ma^r)^(-1)\\\\\ T=518.67(1+(1.4-1)/(2) 0.7625^2)^(-1)\\\\\ T=464.6R\\\\`

`\ velocity \ of \ sound \ (C)=√(KRT)\\\\`

`=√(1.4*1716*464.6)\\\\=1057 ft^3\\\\`

R= gas constant=1716

`m=PAV\\\\`

`=0.001808*0.05*(Ma.C)\\\\=0.001808*0.05*0.7625* 1057\\\\=0.0728(slug)/(s)`