Question

How does surface roughness affect the pressure drop in a tube if the flow is turbulent? What would your response be if the flow were laminar?

Short answer

Answer: Surface roughness significantly affects the pressure drop in turbulent flow, with rougher surfaces leading to higher pressure drops. In contrast, in laminar flow, the impact of surface roughness on pressure drop is negligible, and the pressure drop is primarily determined by fluid viscosity and flow rate.

Step-by-step solution

Define turbulent and laminar flow

Turbulent flow is a flow regime characterized by chaotic, eddying motions where the fluid velocity and pressure fluctuate unpredictably. On the other hand, laminar flow is a regular, smooth flow regime with fluid particles moving in parallel to the tube walls in a series of layers without mixing between them.

Understand pressure drop in a tube

Pressure drop in a tube is a measure of the decrease in fluid pressure along the length of the tube as a result of friction between the fluid and the tube walls. The pressure drop is influenced by several factors, including the fluid's viscosity, the flow rate, the tube's diameter, and the surface roughness of the tube walls.

Effect of surface roughness on turbulent flow

In turbulent flow, surface roughness has a significant impact on pressure drop. The rougher the tube walls, the more energy is dissipated as the fluid encounters increased resistance while flowing through the tube. This leads to a greater pressure drop for a given length of the tube. In turbulent flow, the pressure drop is mainly influenced by the wall shear stress, which is directly related to the roughness of the surface.

Effect of surface roughness on laminar flow

In laminar flow, the effect of surface roughness on pressure drop is generally negligible. Since fluid particles flow in parallel layers without mixing, there is little interaction with the rough tube surface, and the overall frictional resistance is relatively low. Therefore, the pressure drop in laminar flow is primarily determined by viscosity and flow rate, with surface roughness playing a minor role, if any, in pressure drop.

Conclusion

In conclusion, surface roughness significantly affects pressure drop in turbulent flow, with rougher surfaces leading to higher pressure drops. On the other hand, in laminar flow, the impact of surface roughness on pressure drop is negligible, and the pressure drop is primarily determined by fluid viscosity and flow rate.