Critical Depth in Open Channel Flow | Civil Engineering Optional Notes 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)