Show that the discharge Q passing through a pipe of diameter D, as measured by an orifice meter of diameter d, can be expressed as where c is a function of Reynolds number and the ratio between the...

Show that the discharge Q passing through a pipe of diameter D, as measured by an orifice meter of diameter d, can be expressed as

where c is a function of Reynolds number and the ratio between the pipe and orifice diameters, p is the pressure difference on the orifice, and p and v (found in Reynolds number) are the density and kinematic viscosity of the fluid.