Monterey Bay Aquarium Research Institute
Marine Botany

morphp.jpg (20662 bytes)Phycological Methods morphp.jpg (20662 bytes)

Drag Forces

Both surface friction and pressure impose drag forces. For objects as large as most macroalgae, friction drag is much smaller than pressure drag, so we will consider only the later (pressure or form drag). We observed above that as fluid travels around an obstruction, compression of streamlines produces a pressure gradient. Such pressure gradients produce both drag and lift forces.

Pressure drag results from streamwise gradients in velocity and pressure (streamwise means in the direction of flow). Lift stems from a pressure difference between the top and bottom of an object (e.g., an airfoil). In contrast, pressure drag is due to a difference in pressure between the front and the midsection of an object. drawing of drag

Since the streamlines around the midsection of an object are compressed relative to those in front of an object, pressure is higher in front of the object than at its midsection. This gradient in pressure from front to middle results in the exertion of a net force on the front face of the object.

But wait, you ask, isn't there also a gradient in pressure between the middle and back of the object? Certainly. In fact, for a friction-less (inviscid) fluid, the pressure gradients between the front and middle of the object and between the middle and the back are exactly equal. An inviscid fluid exerts no pressure drag.

However, a viscid (sticky) fluid sticks to the surface of the object and this dissipates energy through friction. Frictional dissipation of energy prevents the rear pressure gradient from equaling the pressure gradient on the front face (see all references for further discussion). Ultimately, our net force is still rearwards. net force drawing

An equation similar to the one for lift describes pressure drag.  

Drag Force = 1/2 * r * CD *Aprojected * u2

flow drawing

r = Fluid Density

CL = Coefficient of Drag (proportionality coefficient--empirically determined)

Aplanform = Project Area (in the direction of flow)

u = Fluid Velocity

Once again, higher velocities produce more drag.

Note also that this equation applies only to objects that maintain their shape in flow.  Drag depends on the frontal area presented to flow, so objects that compress in flow decrease drag forces.  A Vogel Number  quantifies the decrease in drag for an organism that "goes with the flow".

© 1999 Elizabeth Nelson, Stanford University Department of Biological Sciences, Hopkins Marine Station. Educational uses permitted.               

Last updated: Feb. 05, 2009