An orifice meter is a device used to measure the flow rate of a fluid in a pipe. It consists of an orifice plate with a small hole (orifice) installed in the pipe, which causes a pressure drop across it. The coefficient of discharge (Cd) is a dimensionless constant used to relate the actual flow rate to the theoretical flow rate predicted by the ideal flow equation.


The coefficient of discharge Cd for an orifice meter is a function of both the diameter of the orifice (d) and the diameter of the pipe (D), as well as the Reynolds number (Re).

1. Effect of d/D:
The ratio of the orifice diameter (d) to the pipe diameter (D) is known as the beta ratio (β = d/D). This ratio plays a significant role in determining the flow characteristics and the coefficient of discharge. The Cd value changes with the beta ratio, as it affects the flow profile and the pressure recovery downstream of the orifice. So, Cd is a function of d/D.

2. Effect of Reynolds number:
The Reynolds number (Re) is a dimensionless quantity used to determine the flow regime in a pipe. It is defined as the ratio of the inertial forces to the viscous forces in the fluid. The Reynolds number is calculated using the fluid properties (density and viscosity), the flow velocity, and the characteristic length (diameter). The flow regime can be laminar or turbulent, and it significantly affects the flow behavior and the coefficient of discharge. So, Cd is also a function of Reynolds number.

3. Combined effect:
The Cd value for an orifice meter is influenced by both the beta ratio (d/D) and the Reynolds number (Re). The interaction between these two factors determines the flow patterns, pressure losses, and the overall flow characteristics. Therefore, the coefficient of discharge Cd is a function of both d/D and Reynolds number.

4. Independence:
The coefficient of discharge Cd is not independent of d/D and Reynolds number. Both these parameters play a crucial role in determining the accuracy and reliability of the orifice meter. Neglecting their influence can lead to significant errors in the flow measurement.


In conclusion, the coefficient of discharge Cd for an orifice meter is a function of both the orifice diameter (d) to pipe diameter (D) ratio (d/D) and the Reynolds number (Re). These parameters affect the flow behavior, pressure losses, and the overall accuracy of the flow measurement. Therefore, the correct answer is option 'C' - Cd is a function of d/D and Reynolds number.