Steady flow in a pipe of uniform cross-section

Steady flow refers to the flow of fluid in a pipe in which the velocity, pressure, and other flow parameters do not change with time. On the other hand, unsteady flow is characterized by time-varying flow parameters. In a pipe of uniform cross-section, the flow can be taken for granted to be steady. This is because the pipe has a constant diameter throughout its length, and the fluid flows through it at a constant rate. The following are the reasons that make flow in a pipe of uniform cross-section steady.

Constant area

In a pipe of uniform cross-section, the area of the pipe remains constant along its length. This means that the volume of fluid passing through the pipe is constant, assuming the fluid density is constant. Therefore, the velocity of the fluid must remain constant to ensure that the flow rate is constant.

Laminar flow

In a pipe of uniform cross-section, the flow of fluid is typically laminar, which means that the fluid flows in layers without mixing. Laminar flow is characterized by smooth, continuous flow, with no turbulence. This type of flow is more likely to be steady than turbulent flow, which is characterized by fluctuations in velocity and pressure.

No external forces

In a pipe of uniform cross-section, the fluid is confined within the pipe, and there are no external forces acting on it. This means that there are no disturbances to the flow, and the flow can remain steady.

Conclusion

In conclusion, steady flow can be taken for granted in a pipe of uniform cross-section because the area of the pipe remains constant, the flow is typically laminar, and there are no external forces acting on the fluid.