Critical Depth in Open Channel Flow | Civil Engineering Optional for UPSC PDF Download

Specific energy concept, which relates the flow depth to the total energy per unit weight of fluid in the channel. The specific energy E for a given flow depth y and flow velocity V is given by: 
where: E is the specific energy (energy per unit weight of fluid), 
V is the flow velocity, 
y is the flow depth, and g is the acceleration due to gravity. 
The critical depth (Y_c) is the flow depth at which the specific energy is at a minimum for a given discharge. At critical depth, the specific energy is minimized, meaning it's the most efficient depth for conveying a given discharge. This is often associated with the maximum flow rate, as any other depth would require more energy for the same discharge. 

Conversely, for a given value of specific energy, the critical depth gives the greatest discharge. This implies that if you want to achieve a certain specific energy with the greatest possible discharge, the critical depth is the optimal flow depth. For rectangular channels, the critical depth, dc ft (m), is given by 

where
d_c = critical depth, ft (m)
Q =  quantity of flow or discharge, ft³/s (m³/s)
B = width of channel, ft (m)