Discharge Rate From Pressurized Tank Equations and Calculator

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Discharge Rate From Pressurized Tank Equations and Calculator

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Discharge Rate From Pressurized Tank Equations and Calculator

If the gas or vapor above the liquid in a tank is at gage pressure p, and the discharge is to atmospheric pressure, the head causing discharge will be

Eq. 1, SI
Head Pressure
h = z₁ - z₂ + p / ( ρ · g )

Eq. 1a, U.S.
Head Pressure
h = z₁ - z₂ + ( p / ρ ) ( g_c / g ) = z₁ - z₂ + p / γ

Preview Discharge From Pressurized Tank Calculator

The discharge velocity can be calculated from Eq. 3 using the increased discharge head calculated from Eq. 1 & 2.

Eq. 2
v_o = C_v ( 2 · g · h )^0.5

Eq. 3
V = C_d · A_o ( 2 · g · h )^0.5

Where

V = volumetric flow rate, ft³/sec, m³/s
A_o = area of discharge orifice, ft², m²
h = adjusted height / depth of head, ft, m
z₁ = elevation of fluid, ft, m
z₂ = elevation discharge nozzle, ft, m
g = gravitational acceleration, 32.2 ft/s², (9.81 m/s²)
g_c = gravitational acceleration, 32.2 lbf-ft/lbf-s², (9.81 kg²/s)
ρ = fluid density lbm/ft³, kg/m³
p = pressure above liquid, lbm/ft², kg/m²
C_v = coefficient of velocity, empirical factor that accounts for the friction and turbulence at the orifice, see Table 1
C_d = Approximate Orifice Coefficients for Turbulent Water, see Table 1
γ = specific weight of fluid lbf/ft³, N/m³

Figure 1 Discharge from a Pressurized Tank

Table 1 Approximate Orifice Coefficients for Turbulent Water

Illustration	Description	C_d	C_v
A	sharp-edged	0.62	0.98
B	round-edged	0.98	0.98
C	short tube* (fluid separates from walls)	0.61	0.61
D	sharp tube (no separation)	0.82	0.82
E	short tube with rounded entrance	0.97	0.98
F	reentrant tube, length less than one-half of pipe diameter	0.54	0.99
G r	eentrant tube, length 2 to 3 pipe diameters	0.72	0.72
H	Borda	0.51	0.98
(none)	smooth, well-tapered nozzle	0.98	0.99

*A short tube has a length less than approximately 3 diameters.

Illustrations for Table 1

Source:

Civil Engineering Reference Manual, Fourteenth Edition
Michael R. Lindeburg, PE