**Practical Problem: **

Pipes vibrate and owing to such vibration the pipe fittings loosen and fluid leaks. For a process plant such leaks are substantial. So insight and understanding are needed to figure out as to how we might stop such unwarranted fluid leakage, which not only adds to the operating cost of the plant but also results in sudden breakdowns that affect productivity and profitability of a plant.

We start our investigation by revisiting he concept of Reynold’s number in an effort to gain insights into the underlying phenomenon.

**Revisiting Reynold’s Number:**

As we know Reynold’s number may be described as the ratio of Inertia Forces/Viscous Forces.

We also know that for Reynold’s number (Re) < 2000 the flow in a pipe carrying a fluid (liquid or gas) is laminar and all the fluid travels in a direction parallel to the pipe axis (being careful to neglect Brownian motion, which leads to a slight blurring of the streak lines of flow).This flow would normally create vibration in the pipe since the pipe selects the particular frequency of its choice (its natural frequency) from a range of frequencies imposed on it by the flow to naturally vibrate (high probability exists that the pipe finds its natural frequency from the range of frequencies imposed by flow of fluid).

When Re > 2000 flow disturbances would probably grow, forming turbulent eddies, so that superimposed on the axial flow, there are circulating eddies of many sized with velocities up to about 1/10 of the axial velocity for a smooth pipe (assumption, which in reality might not be found). This is not very insignificant to cause additional vibration in the pipe, in all probability, perpendicular to the flow of the fluid. However, the effect of these turbulent eddies is to mix up the flow and to create a more uniform profile in the pipe.

The importance of flow similarity is that, for two geometrically similar pipes, the flow behavior will be the same for equal values of Re in each pipe. For example, if we specify, therefore for calibration of a flowmeter, a certain value of Re and a certain pipe geometry, then we know, for sure, that this flow will be well defined.

For Laminar flow, Pressure drop is proportional to Velocity (v) and the resulting profile would be Parabolic.

For Turbulent flow, Pressure drop is proportional to square of Velocity (v) and the resulting profile would be flattened by turbulent mixing (higher entropy).

It is now Interesting to compare the similarity of the above two phenomena with the phenomenon of damping force experienced by objects moving in fluids. Where for low speed damping force is proportional to velocity and for high speeds damping force is proportional to the square of velocity. So, there is equivalent relationship between Pressure Drop and Damping Force. Hence we can conclude that higher the pressure drop (due to higher Re) higher would be the damping force that can significantly alter the vibration patterns of pipe vibrations.

The pressure drop or loss might then be referred to as the ‘velocity head’ that causes pipes to vibrate since absolutely ideal laminar flow is not found in practical applications. Hence turbulent flow exists as default mechanism of flow in pipes.

The pipes subjected to such vibrations (a combination of both low and high frequency vibrations) are stressed at their threaded joints, which automatically loosen up to allow fluid to leak past the open joints,

**Practical solutions:**

1. Hangers that support the pipes might be placed in an axisymmetric manner thereby not allowing the resultant vibration wave owing to fluid flow to travel by effectively breaking up the wave at its origin.

2. Increase the pipe schedule, if that is practically possible for the given conditions.

3. Change the fluid viscosity (generally increase), if practically possible.

4. Use longer length of threaded pipes (to increase the stiffness of the pipe joint).

5. Combine any of the above solutions in a manner found practical in the field.