1. Formula - what is Torricelli's theorem

2. Time required to empty a tank / vessel by gravity flow

Torricelli formula is applied to
calculate tank orifice flowrate. The following formula is Torricelli
equation :

**Equation 1 : Torricelli law - what
is the flowrate through an orifice**

Q=Liquid flowrate at orifice (m3/s)

C=Orifice coefficient (-)

A_{1}=Orifice area (m2)

h=Height of liquid from top of tank to middle of orifice (m)

g=gravity acceleration (m.s^{-2})

g=9.81 m.s^{-2}

C=0.6 for non profiled orifice

A tank has a hole of 10 cm diameter on its side following an incident such as a pipe rupture. The height of liquid above the hole is 5 m. What is the flow of liquid out of the tank ?

STEP 1 : calculate the orifice area

The hole is here circular, thus A1 = π*0.1^{2}/4 = 0.0079 m^{2}

STEP 2 : calculate the liquid flowrate

The liquid height above the middle of the hole is 5+0.1/2=5.05 m.

Q = 0.6*0.0079*(2*9.81*5.05)^{0.5} = 0.047 m^{3}/s
= 168 m^{3}/h

The Torricelli equation can be used to calculate the time required to empty a tank by gravity. Tank emptying time formula :

t_{v}=Time in s to discharge a tank up to the level of the
orifice (s)

H=Height of liquid at t=0 (m)

The tank mentioned in the example in paragraph 2 is considered here. The tank is square, with dimensions of 2m*2m.

STEP 1 : calculate the area A_{0}

The tank is square, this A_{0} = 2*2 = 4 m^{2}

STEP 2 : calculate the time required to empty the tank

The liquid height above the middle of the hole is 5+0.1/2=5.05 m. A_{1}
has been calculated in the previous example.

t_{v} = 4/(0.6*0.0079)*(2*5.05/9.81)^{0.5} = 861 s

**Source**

Mecanique et Rheologie des fluides en genie chimique, Noel Midoux, Lavoisier Tec et Doc, page 51