What is torricelli'slaw? Explain how the speed of efflux is determined with an experiment.

Explanation

Torricelli's law: Torricellis discovered that the speed of efflux from an open tarik is given by a formula identical to that of a freely falling body. The word efflux means 'fluid out flow'

Determination of speed of Efflux: Consider a tank containing a liquid of density `'rho'` with a small hole at a height `,y_1'` from the bottom as shown in the figure.
The air above the liquid, whose surface is at height `'y_2'` is at pressure P.
From the equation of continuity , we have
`V_1A_1=V_2A_2impliesV_2=A_1/A_2V_1......(1)`
It the cross sectional area of the tank, `A_2` is much larger than that of the hole `(i.e.,A_2ltltA_1)` , then we may consider the fluid to be approximately at rest at the top i.e., `V_2=0`
Now applying the Bernoulli equation at points (1) and (2) and noting that, at the hole `P_1=Pa`, the atmospheric pressure, we get
`Pa+1/2rhov_1^2+rhogy_1=P+rhogy_2`
Taking `y_2-y_1=h`, we have
`V_1=sqrt(2gh+(2(P-Pa))/rho).....(2)`
When `p lt lt pa` and 2gh may be ignored, the speed of efflux is determined by the container pressure. Such a situation occurs in rocket propulsion. On the other hand if the tank is open to the atmosphere, the P=Pa and from eq(2) , we get
`V_1=sqrt(2gh)`........(3)
This is the speed of freely falling body, at any point of height 'h' during its fall. This equation is known as "Torricelli's law".