Enter the vertical distance, horizontal distance, and constant head water into the calculator to determine the coefficient of velocity.

Coefficient of Velocity Formula

The following equation is used to calculate the Coefficient of Velocity.

Cv = SQRT (x^2 / (4*y*h) )
  • Where Cv is the coefficient of velocity
  • x is the horizontal distance
  • y is the vertical distance
  • h is the head of water

To calculate the coefficient of velocity, square the horizontal distance, divide by the product of 4 times the vertical distance and water head, then take the square root of this result.

How to Calculate Coefficient of Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate Coefficient of Velocity.

First, determine the horizontal distance . In this example, the horizontal distance is found to be 3ft.

Next, determine the vertical distance . For this problem, the vertical distance is found to be 2ft.

Next, determine the head of water . In this case, the head of water is measured to be 4ft.

Finally, calculate the Coefficient of Velocity using the formula above:

Cv = SQRT (x^2 / (4*y*h) )

Cv = SQRT (3^2 / (4*2*4) )

Cv = .530


What is the significance of the coefficient of velocity in fluid dynamics?

The coefficient of velocity is a dimensionless number that measures the efficiency of flow of a fluid through a conduit, nozzle, or other types of flow channels. It is used to determine how much the actual velocity of a fluid deviates from the theoretical velocity, helping engineers and scientists to design more efficient systems by understanding energy losses in fluid flows.

How do changes in the head of water affect the coefficient of velocity?

Changes in the head of water directly affect the coefficient of velocity because the head of water (h) is a critical component of the formula used to calculate it. An increase in the head of water generally increases the potential energy available to the fluid, potentially increasing its velocity if other factors remain constant. However, the actual impact on the coefficient of velocity depends on the relationship between all variables (x, y, and h) in the specific situation.

Can the coefficient of velocity be greater than 1?

In theory, the coefficient of velocity is a ratio of actual velocity to theoretical velocity and should ideally be equal to or less than 1, since it is rare for actual conditions to perfectly match theoretical predictions due to energy losses. A coefficient of velocity greater than 1 suggests that the actual velocity of a fluid exceeds the theoretical predictions, which might indicate an error in measurements or calculations, or specific conditions that enhance the fluid’s velocity beyond expected parameters.