Written Examples

Laminar boundary Example

Question:

Water flows over a 3m long plate with a free-stream velocity of 2m/s at 50℃. Find the drag force acting on the plate per width.

Density and dynamic viscosity of water at 50℃ are ⍴= 988 kg/m3 and μ=0.5471 x10-3 kg/m.s

Solution:

First the Reynolds number needs to be found:

This shows flow is laminar since the Reynolds number is less than the critical value of 105.

Now the Drag coefficient for the plate needs to be calculated and from this the drag per width can be found:

Drag force on a Pipe Example

Question:

A pipe with outer diameter 3cm runs through a 10m wide river. The average flow of water around the pipe is 6m/s at 10℃. Find the drag force acting on the pipe.

Density and dynamic viscosity of water at 10℃ are ⍴= 999.7 kg/m3 and μ=1.307 x10-3 kg/m.s

Solution:

First the Reynolds number of the fluid round the pipe needs to be calculated:

CD=1 at this Re for a cylinder, so now the drag force on the pipe can be calculated: