Water Flowing (Discharging) from a Tank |
Calculation and equations |

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Either the free discharge orifice or the submerged orifice can be modeled. The
equations are the same for both cases. A pull-down menu allows you to select circular
or square orifice geometry. For a circular orifice, B is orifice diameter. For a square
orifice, B is orifice width and height. A pull-down menu allows you to select an orifice
type. Discharge coefficients for the four orifice types are built into the
calculation. User-defined discharge coefficients are permitted but be sure that C_{o}=
C_{c}C_{v}. The calculation only checks to see if inputs are
positive; we do not check to see if C_{o}= C_{c}C_{v}.

**Built-in values for orifice discharge coefficients are:**

Rounded
Sharp-edged
Short tube
Borda

C_{c} 1.0
0.62
1.0
0.52

C_{v} 0.98
0.98
0.8
0.98

The short tube C values are valid for L ~ 2.5 B.

The Borda type is also known as a re-entrant since it juts into the tank.

C values were obtained from Dally et al. (1993) for circular orifices. However,
similar values for square orifices are given in Davis (1942), so our calculation uses the
Dally values for both circular and square orifices.

**Equations**. from Dally et al. (1993) and Streeter et al. (1985)

These equations are valid for: H > 1.25 m (4.17 ft) and B >
2.54 cm (1 inch). Values will be computed even if H or B is too small, but a warning
message will appear.

where: A = orifice area, B = orifice diameter or width and height, C_{c}
= contraction coefficient, C_{v} = velocity coefficient, C_{o} = orifice
coefficient = C_{c}C_{v}, g = acceleration due to gravity = 32.174 ft/s^{2}
or 9.8066 m/s^{2}, H = head defined in diagrams above, Q = flowrate (discharge), V
= horizontal velocity through orifice, X = horizontal trajectory, Y = vertical trajectory.

References

Dally, J. W., W. F. Riley, and K. G. McConnell. 1993. Instrumentation for
Engineering Measurements. John Wiley and Sons, Inc. 2ed.

Davis, C. V. 1942. Handbook of Applied Hydraulics. McGraw-Hill Book Co.

Streeter, V. L., E. G. Wylie, and K. W. Bedford. 1985. Fluid Mechanics.
McGraw-Hill. 9ed.

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(Sept. 2, 2008: re-arranged page)