Wavespeed and Communication Time

Wavespeed

The speed at which a wave propagates throughout a medium is termed the wavespeed. The wavespeed depends on the acoustical velocity of the fluid itself as well as the physical properties of the pipe and the method of support.

Acoustical velocity through the fluid is related to the bulk modulus of elasticity (K) and density (ρ) of the fluid.

This wavespeed is the propagation speed in a fluid where there is no mechanism to impede the wave motion - for example, in an unbounded body of fluid or in a completely rigid pipe.

In piping systems, some of the energy in a pressure wave distorts the pipe itself, reducing the wavespeed. This depends on the pipe modulus of elasticity (E), the inner diameter (D), the wall thickness (e) and a constant (c₁) which depends on pipe supports.

For more information, see Wavespeed - Detailed Discussion.

Also note that the wavespeed equation presented here is only valid for fluids with no solids present. If the SSL Module is being used to model settling slurries, the wavespeed is adjusted as is discussed in the Wavespeed Calculation for Slurries topic.

Communication Time

An important consideration in fluid transient studies is how long it takes a wave to propagate through the system.

The time it takes for a wave to travel from one end of a system to the other is simply the distance (L) divided by the wavespeed.

When a transient event occurs at one end of a pipe, the wave travels at the wavespeed to the other end of the pipe. However, this is not sufficient time to analyze the problem. While the disturbance has propagated through the entire system, the point of transient initiation has not yet seen the result of the reflected wave. For the wave to both travel to the end of the pipe and back requires double the above time. This time is known as the Pipe Period or Communication Time.

Note: The Communication Time only accounts for half of the wave cycle (described in the Conceptual Example). This is how much time it takes for a disturbance to return to its starting point, but analyzing a system for only this amount of time neglects part of the transient cycle. Transient simulations should run for at least double the Pipe Period, or 4L/a.