From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
The equations for the flow of gases through an orifice.
| Identifier | ExFiles\Box 36\1\ scan 019 | |
| Date | 18th February 1916 | |
| -7- X. 2907 - G/O.{Mr Oldham} FLOW OF GASES THROUGH ORIFICES. The flow of a gas through an orifice (or restriction) from a vessel at a pressure P1 (lbs per sq.ft) to external space at a pressure P2 (lbs"sq.ft) is given by the following equation :- W = CA * sqrt[ (2gn/(n-1)) * (P1/V1) * {D^(2/n) - D^((n+1)/n)} ] when D is greater than a certain limiting value, and by the equation :- W = CA * sqrt[ gn * (P1/V1) * (2/(n+1))^((n+1)/(n-1)) ] where D is less than this value, where :- W = mass of gas flowing through orifice (pounds per sec) C = Coefficient of discharge (= coeff. of contraction x coeff. of velocity) A = Area of cross section of orifice (sq.ft) g = 32.19 ft.per sec.per sec. n = index of expansion of gas through orifice. (The expansion is practically adiabatic for a sharp orifice, but n will have a lower value than the adiabatic value if the orifice has appreciable length). P1 = internal pressure (lbs. per sq.ft) V1 = specific volume of gas in vessel (cubic ft. per lb) D = pressure ratio P2/P1 If we keep the internal conditions the same and vary the external pressure P2, i.e. vary the fraction D, the mass of dis- charge per second will vary, or remain constant depending upon the actual value of P2 in relation to P1. Contd. | ||