What is the force imposed by underwater currents?

Question

I would like to calculate the force of an underwater current on a meter by meter plate (or any other unit that you may use to represent it) that is standing in front of the current. How do I calculate it? What parameters do I need?

Answer 1

You are looking for the drag force imposed by the fluid flow on an object:

$$F = \dfrac{1}{2} \rho v^{2} C_D A$$

where $\rho$ is the density of the fluid, $v$ is the speed of the flow, $C_D$ is the drag coefficient depending on the shape of the object, and $A$ is the surface area normal to the fluid flow.

Let's plug in some characteristic numbers for scaling. For a current of 1 m s$^{-1}$, fluid density of 1000 kg m$^{-3}$, drag coefficient of 1, surface area of 1 m$^2$, the force imposed by the fluid on the object, according to the equation above, would be 500 N.

Note that this equation is valid only for high $Re$ flows that produce turbulence in the wake of the object. The drag coefficient is estimated empirically and takes into account both skin and form drag of the object.