Engineering
Torricelli's Law tank orifice velocity SQRT(2gh) & discharge flow (L/s)
Calculate ideal gravity efflux velocity SQRT(2*g*h) and real orifice volumetric discharge Cd * Area * SQRT(2*g*h) in liters per second.
Estimate instantaneous discharge from a specified liquid head
Torricelli speed sqrt(2gh) assumes incompressible flow from a large tank, negligible free-surface velocity, equal pressure at the free surface and outlet, and head measured to the opening center. This is an instantaneous calculation at the specified head; draining changes head and flow over time.
Estimate flow as Cd*area*sqrt(2gh). Cd is an empirical coefficient accounting for contraction and losses, not a universal nozzle constant. The supplied 0.62 and 0.98 are illustrative. At Cd=0.62, corrected flow is 38% below the ideal flow; conversely ideal flow is about 61% above the corrected estimate. This is not an exact calibrated discharge measurement.
| Tank Orifice Parameter (Head h = 5 m, d = 0.05 m, Cd = 0.62) | Formula | Result |
|---|---|---|
| Ideal Torricelli Jet Velocity (m/s) | SQRT(2 * 9.81 * 5) | 9.90 m/s |
| Circular Orifice Area (m^2) | PI() * (0.05 / 2)^2 | 0.001963 m^2 |
| Estimated discharge flow (L/s) | 0.62 * Area * 9.9045 * 1000 | 12.06 L/s |
| Rounded Bellmouth Nozzle (Cd = 0.98) | 0.98 * Area * 9.9045 * 1000 | 19.06 L/s |
Ideal Torricelli efflux velocity (m/s)
A2=LiquidHead_m (5) and B2=Gravity_m_s2 (9.81).
=IF(OR(COUNT(A2:B2)<>2,A2<0,B2<=0),"Invalid inputs",ROUND(SQRT(2 * B2 * A2), 2))Estimated volumetric discharge (L/s)
C2=OrificeDiameter_m (0.05) and D2=DischargeCoeff Cd (0.62); * 1000 converts m^3/s to L/s.
=IF(OR(COUNT(A2:D2)<>4,A2<0,B2<=0,C2<=0,D2<=0,D2>1),"Invalid inputs",ROUND(D2 * PI() * ((C2 / 2) ^ 2) * SQRT(2 * B2 * A2) * 1000, 2))Try the example
Use the original values or change them to test your understanding.