The drag force acting on a body moving through an external fluid flow is characterized by two different drag effects: the skin friction drag, due to viscous flow parallel to the surface of the object, and the pressure drag, due to the pressure gradient induced around the object. Drag is complicated to calculate and depends on factors such as fluid viscosity, object geometry, temperature, compressibility, surface roughness, velocity, turbulence, pressure, and so on. It is often more expedient to use general dimensionless parameters based on geometry and flow conditions to find the drag force. These parameters are known as the drag coefficients.

Skin friction drag depends on the fluid flow regime—meaning whether the flow is laminar or turbulent. For a flat plate, the flow regime can be estimated using the Reynolds number, using the equation

where x is the length of the plate in the direction of flow.

The coefficient of drag for skin friction drag, known as the friction drag coefficient, is found by the equations

Depending on the fluid flow regime.

The force of drag due to skin friction can then be estimated by

where C_(D,f) is the friction drag coefficient, and A is the area of the surface parallel to the direction of flow.

The coefficient of drag for pressure drag, known as the pressure drag coefficient, is often determined experimentally. For common simple geometric shapes, the pressure drag coefficients based on the type of shape and its dimensions are widely known.

The force of drag due to pressure can be estimated by

where C_(D,p) is the pressure drag coefficient, and A is the total frontal area perpendicular to the direction of flow.

The UUV can be roughly modeled using simple geometric shapes and surfaces to find a drag force estimate when it moves through the water, during the conditions specified in the design requirements. Figure 39 below shows the simple model used for rough drag force calculations, as seen when looking at the port (left-hand) side of the UUV. Table 5 gives the properties of each object in the model.

Plugging in Variables

The surging flow (V_u) is 1.0 m/s, and the heave flow (V_w) is 0.2 m/s. The density of seawater ρ is 1027 kg/m^3, and its viscosity μ is 0.00141 kg⁄(m∙s).

Using these values, the Reynolds numbers can be calculated for flow in the surge (u) and heave (w) directions using Equation 11:

Since Re_u and Re_w are less than 5∙10^5, it can be assumed that flow is laminar. The friction drag coefficients in the surge and heave directions can then be calculated using the drag coefficient equation for laminar flow:

Using these values, the net drag force in each direction can be estimated as

by adding each modeled object’s area and drag coefficient to obtain an effective drag coefficient for that direction of flow, which evaluates to