If laminar flow takes place in two pipes, having relative roughnesses of 0.001 and 0.002, then

To determine if laminar flow occurs in two pipes with relative roughnesses of 0.001 and 0.002, we can use the Reynolds number. The Reynolds number is a dimensionless quantity that characterizes the flow regime.

The Reynolds number (Re) is calculated using the formula:

Re = (velocity * diameter) / kinematic viscosity

where velocity is the flow velocity, diameter is the pipe diameter, and kinematic viscosity is the viscosity of the fluid divided by its density.

For laminar flow, the Reynolds number should be less than a critical value, typically around 2000. If the Reynolds number is greater than this critical value, turbulent flow is likely to occur.

Let's calculate the Reynolds number for each pipe:

For the first pipe with a relative roughness of 0.001, we need to know the flow velocity, pipe diameter, and kinematic viscosity of the fluid. Once we have these values, we can substitute them into the Reynolds number formula to calculate the Reynolds number.

Similarly, for the second pipe with a relative roughness of 0.002, we follow the same steps to calculate the Reynolds number.

After calculating the Reynolds numbers for both pipes, we compare them to the critical value of 2000. If the Reynolds number is less than 2000 for both pipes, it indicates that laminar flow is taking place. If the Reynolds number is greater than 2000 for either pipe, turbulent flow is likely occurring.

Therefore, by calculating the Reynolds numbers for the two pipes, we can determine if laminar flow is present.