How is velocity head mathematically expressed?

• A. V²/2g
• B. 2g/V²
• C. g²/2V
• D. 2V/g

Answer: (A)

Velocity head is a crucial concept in fluid mechanics that represents the height of a fluid column that would produce a certain velocity in the fluid. It is derived from the kinetic energy of the fluid per unit weight.

Mathematically, the velocity head is expressed as the dynamic pressure of a fluid divided by the weight density of the fluid. Specifically, it can be calculated using the formula:

[ \text{Velocity head} = \frac{V^2}{2g} ]

In this formula, ( V ) represents the velocity of the fluid, and ( g ) is the acceleration due to gravity. By squaring the velocity and then dividing by twice the gravitational acceleration, you obtain a measurement that indicates the kinetic energy per unit weight of the fluid as a height.

This relationship is significant in various applications within water treatment and fluid dynamics, as it helps in assessing the energy changes that occur in fluid systems. Understanding velocity head is essential for engineers and technicians in optimizing flow rates and ensuring efficient operation in water treatment facilities.