Which formula is used to determine the discharge coefficient relating pressure and flow rate?

The discharge coefficient is a critical parameter in fluid dynamics that relates the flow rate of a fluid to the pressure drop across a device, such as a valve or an orifice. The correct formula, where the discharge coefficient ( K ) is defined as the flow rate ( Q ) divided by the square root of the pressure ( P ), effectively captures how pressure influences flow characteristics.

This relationship arises because, according to fluid dynamics principles, flow rate is influenced not just directly by pressure but by the dynamic attributes of flow that can be expressed as a function of pressure. The square root of pressure reflects the kinetic energy conversion from the pressure energy, hence allowing for a more precise measurement of the impact of pressure on flow rate.

Using the other formulas misrepresents how flow rate and pressure interact. The incorrect formulas would either not incorporate the correct mathematical relationship or misrepresent the dynamics of fluid flow in pressurized systems. Thus, the choice that utilizes the square root function demonstrates a foundational understanding of the underlying physics governing flow behavior and the continuous relationship between pressure and flow rates in water-based systems.