Rectangular Weir Flow Rate Calculator

Rectangular weir flow calculator 

Utilize the advanced mechanics’ rectangular weir flow calculator to find the rate at which the water flows through the weir spillway in cubic meters per second.

What is a rectangular weir?

A weir is a form of obstruction installed across a river to modify its flow dynamics. It's often utilized for flood control, gauging water outflow, and ensuring rivers are suitable for navigation.

A rectangular weir is one of the simplest designs, essentially a flat barrier with a rectangular notch cut out from the top where water can flow over.

Other most commonly used types of weirs include v-notch and triangular weirs.  

Rectangular weir flow rate formula:

The flow rate (Q) over a rectangular weir can be calculated using the formula:

Q = Cd * L * H^n

where:

• Q is the flow rate.
• Cd is the discharge coefficient (which accounts for energy losses in the flow and depends on the physical characteristics of the weir; for a perfect rectangular weir, Cd is approximately 3.33 when using feet and seconds, and 1.84 when using meters and seconds)
• L is the width of the notch (in feet or meters)
• H is the head over the weir (in feet or meters), which is the height of the water above the bottom of the notch.
• n is the head exponent, typically taken as 1.5

The flow is considered free-flowing (as opposed to submerged or drowned) if the water downstream of the weir is at a lower height than the crest. This formula for Q assumes free-flowing conditions.

How to calculate the flow rate of a rectangular weir?

The formula to find the flow rate is mentioned above. The width and head can be measured using measuring tools while the head exponent and discharge constant are constant for the perfectly rectangular weirs. Otherwise, these two need to be calculated as well.

Example: 

Let's assume a rectangular weir with the following dimensions:

Width of the notch (L): 2 meters

Height of the water above the bottom of the notch (H): 0.5 meters

And typical value for the discharge coefficient (Cd) in metric units: 1.84

Step 1: Plug these into the formula for the flow rate over a rectangular weir.

Q = Cd * L * H^n

We have:

Q = 1.84 * 2 * (0.5)^1.5

Step 2: Calculate H^n:

(0.5)^1.5 = 0.354

Step 3: Multiply this by Cd and L:

Q = 1.84 * 2 * 0.354 = 1.30176 cubic meters per second

So, with these parameters, the flow rate over the weir would be approximately 1.30 cubic meters per second.