Rate of change of pressure

In summary, the pressure changes over a fixed interval of time (del t1) and pressure changes over another fixed interval of time (del t2) at x=0, where del t1 = del t2.
  • #1
sarahh
5
0
Dear Sir/Madam,

I would like to know if I can apply the conservation of momentum to the rate of change of pressure at a fixed position (for e.g. x=0) as follows:
dP1/dt=-dP2/dt

where dP1 is the pressure changes over a fixed interval of time (del t1) and dP2 is the pressure changes over another fixed interval of time (del t2) at x=0, and del t1 = del t2.

Can I explain the above equation as follows:
at x=0, pressure increases by dP1 in del t1 and this dP1/dt is balanced by an equivalent negative rate of momentum changing force per unit area, -dP2/dt after certain period of time.

Thank you very much for your kind assistance.

Sarah
 
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  • #2
The conservation of momentum does not apply at all.

Perhaps you should tell us the entire problem you're trying to solve?

- Warren
 
  • #3
Urgent, Please Help

Thank you for the reply.

Our problem is that we measured the rate of change of pressure of a liquid at different length of a pipe, for example, x=0, x=5cm, ... etc, caused by a pump at x=0-15cm=-15cm and got a result that at x=0, dP1/dt1 = -dP2/dt2, where dP1 is the pressure difference over a fixed interval, del t1, and dP2 is the pressure difference over a fixed interval, del t2,
i.e. -----------
- -
- -
del t1 |3 minutes | del t2
(just like a trapezium without the bottom part), and del t1=del t2. Pumping power is decreasing from t=0 to t=4minutes and pumping power =0 when t>4 minutes.
Is it accurate if we try to explain this observation as follows:
Due to conservation of momentum, the rate of momentum-changing force per unit area, dP1/dt, produced by the pump is balanced by an equivalent negative rate of momentum-changing force per unit area, -dP2/dt produced by the system after 3 minutes at x=0.

Thanks again!

Sarah
 
Last edited:
  • #4
Does the cross-sectional area of the pipe change? I would think that if you assume the fluid to be relatively incompressable then you could use Bernoulli's Equation to say that the pressure of the fluid at any point along the tube would be the same (so long as the area of the tube does not change) after the application of the impluse due to the pump. Isn't this just a description of a longitudinal wave in a fluid, a result of the impluse applied by the pump?
 
  • #5
Yes, the cross-sectional area of the pipe changes along the x-direction. We would like to study the relationship between the rate of change of pressure and the rate of change of pumping power.

Sarah
 
  • #6
I think Bernoulli's Equation still applies here. It relates the speed of a fluid to the pressure in the pipe. How are you measuring things?
 

1. What is the rate of change of pressure?

The rate of change of pressure refers to how quickly the pressure of a system is increasing or decreasing over time. It is a measure of how much the pressure is changing in a certain amount of time.

2. How is the rate of change of pressure calculated?

The rate of change of pressure can be calculated by taking the difference between the initial and final pressure values and dividing it by the time interval between the two measurements. This is represented by the formula: rate of change of pressure = (final pressure - initial pressure) / time interval.

3. What causes a change in pressure?

A change in pressure can be caused by a variety of factors, such as temperature, volume, and the amount of gas or liquid in a system. For example, increasing the temperature of a gas will cause its particles to move faster and collide with the container walls more frequently, resulting in an increase in pressure.

4. How does the rate of change of pressure affect a system?

The rate of change of pressure can have a significant impact on a system. A rapid change in pressure can cause explosions or implosions, while a slow change in pressure can affect the stability and function of a system. It is important to monitor and control the rate of change of pressure in order to maintain safe and efficient operation of a system.

5. What units are used to measure the rate of change of pressure?

The rate of change of pressure is typically measured in units of pressure per unit of time, such as psi/s (pounds per square inch per second) or Pa/s (pascals per second). Other common units include kPa/s, bar/s, and mmHg/s. The specific unit used may depend on the type of system and the application.

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