# Calculating viscous drag in water

1. Nov 19, 2005

### Dan Moskal

Hello:

Need some help here.

I am trying to Calculate the viscous drag for a body traveling through water at given velocity and wetted surface area. At this time I am not trying to calculate the pressure drag or wave drag.

Basically what I want to know is how many newtons of force are absorbed by the viscous drag only.

I know the basic equation is

Rf = 0.5v^2s , where Rf is the viscous drag, v is velocity and s is the wetted surface area.

What I don't understand is how much force does Rf represent? Is it in Newtons?

Also, is the Rf related to the Coefficient of drag (Cf)? I know the Cf is pressure drag related to the shape of the object, for example about 0.295 for a bullet shaped object. Can you use the Rf in equations that call for the Cf?

Is the Rf related to the Re (Reynolds number)? How do you use the Reynolds number to help calculate the viscous drag losses on a surface area?

I am also confused because the equation Rf = 0.5v^2s does not take into account the temperature of the water. Viscosity varies alot with temperature.

Any help appreciated. To make the math simpler, assume fresh water with a density of 1.0.

Dan

2. Nov 12, 2006

### scramjet

Viscous drag (Rf) depends on the following:

wetted surface area - S (m^2)
speed of the hull - V (m/s)
viscosity (mu)
kinematic viscosity (nu)
density of water (rho)
coefficient of friction- Cf no units
length of waterline- L(m)
Rf = 0.5 x (rho) x V^2 x S x Cf
in units -> kg/m^3 x (m/s)^2 x m^2 = kg x m/s^2 = mass x acceleration = force

3. Nov 13, 2006

### Hawknc

There are a number of drag coefficients, each of them relating to the specific drag that you're calculating at the time. Scramjet posted the correct equation for calculating skin friction.

The Reynolds number is important because it gives you an idea of the ratio of viscous forces to inertial forces, and thus how important skin friction is. It basically determines whether your boundary layer (the water flow very close to the object, where the flow is slowed down because of skin friction and viscosity) is laminar i.e. smooth, or turbulent. There's different approximations for skin friction coefficients in each case, and the flow may change from laminar to turbulent part of the way along the hull.

In short, you've picked up on a rather complex topic. ;) There's no exact answer. Reasonable estimates can be gleaned from the Blasius approximation (for laminar) and the 7th-root approximation (for turbulent), but they don't take into account surface roughness, which is a lot more important in water than it is in air. Unfortunately you'd have to work that out experimentally, but as I said earlier, you can get a good rough estimate based on boundary layer approximations.