Coefficient of Discharge Calculator

The discharge coefficient is the ratio of theoretical and actual flow rate. The discharge coefficient is a one-dimensional parameter. It is one of three hydraulic coefficients, the others being:

• Cd = Coefficient of discharge
• Cc = Coefficient of contraction
• Cv = Coefficient of velocity

The coefficient of discharge is concerned with the flow rate, whereas the coefficient of contraction is concerned with the change in the cross-section and jet area. Finally, the coefficient of velocity is related to the actual and theoretical velocities of a fluid jet. The equation below connects the three hydraulic coefficients.

Cd = Cv x Cc

Orifice, venturi, weir, open-channel flows, and other discharge coefficients

Consider a fluid flow that has the same cross-sectional area at all times. The discharge coefficient Cd, is as follows: Cd = Qact/ Qth

• Where Qact = Actual discharge
• Qth = Therotical discharge

At one end of the orifice, the actual discharge can be measured and denoted as m(dot) or Qact. On the other hand, the theoretical discharge is provided by the equation:

Qth ΓÇï =ρAc=A (2ρΔP)^(½) ΓÇï =A (2gH)^(½) ΓÇï

• Where, ρ = Density of fluid
• A = Area of cross-section;
• c = Flow velocity;
• ΔP = Change in pressure;
• g = Acceleration due to gravity; and
• H = Head of fluid.

As a result, the coefficient of discharge is: Cd = Qact/ Qth = Qact/A (2gH)^(½) ΓÇï

The discharge coefficient is usually between 0.6-0.65 in most circumstances. The flow resistance, or resistance provided by the environment in which the fluid flow occurs, is similarly connected to the discharge coefficient. The flow resistance, kk, is proportional to the discharge coefficient as follows: k = 1/Cd^2

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To find out how much theoretical discharge you'll get if you use the following formula:

• Step 1: Calculate the hydraulic head by multiplying it by the gravitational acceleration.
• Step 2: Multiply the answer by two to get the final result.
• Step 3: Calculate the product's square root
• Step 4: To calculate the theoretical discharge for a fluid flow, multiply the obtained value by the cross-sectional area.

You'll need a stopwatch and a bucket with the known capacity to determine the actual discharge.

• Step 1: Start flowing the fluid.
• Step 2: As the bucket begins to fill, set the timer.
• Step 3: When the bucket is completely full, turn off the timer.
• Step 4: To calculate the actual discharge, multiply the bucket's capacity by the time period.

To find the discharge coefficient, use the following steps:

• Step 1: Multiply the hydraulic head by the gravitational acceleration.
• Step 2: Multiply the result by two to get the final result.
• Step 3: Find the product's square root.
• Step 4: To get the theoretical discharge for a fluid flow, multiply the result by the area of cross-section.
• Step 5: To calculate the discharge coefficient, divide the actual discharge by the theoretical discharge.

1. What is the purpose of calculating the coefficient of discharge?

This parameter can be used to calculate the irrecoverable losses caused by a piece of equipment (constriction) in a fluid system, as well as the "resistance" that piece of equipment imposes on the flow.

2. What is a typical discharge coefficient?

A discharge coefficient of cd = 0.975 can be used as a benchmark, however, the value varies significantly at low Reynolds numbers. The pressure recovery of the venturi meter is substantially better than that of the orifice plate.

3. What is the discharge coefficient of a weir?

Broad-crested weir and short-crested weir are two types of low weirs with a flat top. The discharge coefficient of a short-crested weir is around 0.33–0.46 under the same inflow scenario, whereas the discharge coefficient of a broad-crested weir is 0.32–0.385, indicating that the former is greater than the latter in terms of discharge capacity.