Explanation:

A broad crested weir is a hydraulic structure constructed across an open channel to measure the flow rate of water. The depth of water at the end of the sill is given by the following formula:

h = H/2

Where,
h = Depth of water at the end of sill
H = Height of the weir

The above formula is derived using the concept of energy conservation. The velocity of water at the end of the sill is zero (v = 0) and the pressure head is atmospheric (P = 0). Therefore, the total energy at the end of the sill is equal to the water surface elevation (z) at the upstream side of the weir.

The total energy at the end of the sill is given by the following formula:

E = z + h

Where,
E = Total energy
z = Water surface elevation at the upstream side of the weir

The total energy at the upstream side of the weir is given by the following formula:

E = y + V^2/2g

Where,
y = Water surface elevation at the upstream side of the weir
V = Velocity of water at the upstream side of the weir
g = Acceleration due to gravity

At the end of the sill, the velocity of water is zero (v = 0) and the pressure head is atmospheric (P = 0). Therefore, the total energy at the end of the sill is equal to the water surface elevation (z) at the upstream side of the weir.

E = z

Equating the above two expressions for total energy, we get:

z + h = y + V^2/2g

Since the velocity of water at the end of the sill is zero (v = 0), we have:

V^2/2g = 0

Therefore, the above equation reduces to:

z + h = y

Rearranging the above equation for h, we get:

h = y - z

Substituting the value of y - z from the weir equation, we get:

h = H/2

Therefore, the depth of water at the end of the sill in case of a broad crested weir is given by:

h = H/2