# I What really is bandwidth?

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1. Apr 27, 2017

### CyberneticsInside

Hello, I am reading a book about simulation, modeling and automatic control.
In a chapter about hydraulic transmission line, a pipe's "bandwidth" is mentioned.
Contex:
"Long pipes are used in large hydraulic installations where pipes of length up to 10 m are not uncommon. Moreover, in offshore oil and gas production pipes of several hundred meters may be used. A propagation time of T = 10ms will result if L = 10m. This introduces a time delay that may be significant if bandwidths up to 100 rad/s are required"

I am used to bandwidth in the context of data transfer, but not in fluid mechanics. Can someone be so kind to explain the matter to me?

2. Apr 27, 2017

### scottdave

In hydraulic systems, it is data transfer, in a sense. If you want something to happen, then you tell an actuator to open a valve and the fluid flows in, and then downstream, some action will take place. Being aware of the time delays can be critical to how the whole system operates. I found this document, which gives electrical analogies to several fluid components. You may find it interesting. http://engineering.nyu.edu/mechatro...SenActinMecha/S&A_Hydraulics_Pneumatics_1.pdf

3. Apr 27, 2017

### rcgldr

100 radians per second is an "angular" frequency and corresponds to a linear frequency of about 15.9155 hz.

I'm not sure why angular frequency is being used in that book.

Normally bandwidth is independent of propagation delay, so I'm not sure why the book mentions that propagation delay can affect bandwidth, or why an angular frequency constant (100 radians / second) was mentioned.

4. Apr 27, 2017

### scottdave

Yes, it does seem odd to use radians per sec, rather than cycles per second.

5. Apr 28, 2017

### CWatters

It's been a long time since I did any control theory but when you try to stabilize a control system that has time delays in it you usually end up reducing the frequency response of the system (eg reducing the bandwidth).

http://users.ece.utexas.edu/~buckman/H3.pdf
https://uk.mathworks.com/help/control/examples/analyzing-control-systems-with-delays.html

6. Apr 28, 2017

### CWatters

Presumably they arrived at that figure by approximating the speed of sound in water to 1000m/s ?

Might get a better answer in the Engineering part of the forum?

7. Apr 28, 2017

### CyberneticsInside

Thanks, yes thay assume c = 1000 m/s.

8. Apr 28, 2017

### FactChecker

Automatic controls are usually studied in terms of the system response to different frequencies. Suppose the system being studied has problem frequencies above 100 rad/sec. Then you would have to model any delays from pipes of length 10m or longer.

9. Apr 29, 2017

### Paul Colby

A linear amplifier like an op amp has a bandwidth which is intentionally imposed to stabilize the design. Because there is a delay in the output of the amplifier there is a phase change associated with the delay which will flip the sign of the feedback interior to the amplifier. If the gain at $f_o$ is greater than 1, one has an oscillator rather than an amplifier. This is fixed by reducing or rolling off the gain above $f_o$, or, limiting the bandwidth to be 0 to $f_o$. The same issue is dealt with in any feedback (aka control) system. The propagation delay will limit the bandwidth of the control loop it appears in.