Laminar and turbulent flow

In the nineteenth century Reynolds investigated the conditions that would give turbulence in the flow of a fluid. He showed that the velocity for liquid flow in a tube is given by:

V_c = R_eη/2ρr

where η is the viscosity of the liquid and ρ its density, and r the radius of the tube. The constant R_e is the Reynolds number.

It can be found from experiment that if R_e < 2000 the flow is streamlined (laminar), if R_e~ > 3000 the flow is turbulent and if it lies between these two the flow is unstable. The flow of liquid can easily be demonstrated with the apparatus shown in Figure 1.

A dye flows from the tube into the tank and by altering the pressure head the flow can be made either turbulent or laminar.

As you can see from the graph in Figure 2, the flow becomes turbulent when the line ceases to be straight.

The streamlining of bodies is most important in the design of cars, submarines and the nose cones of aircraft and rockets since a reduction in drag can reduce vibration and also save large amounts of fuel. Figure 3 shows the best shapes for rocket cones for subsonic, supersonic and hypersonic flight.