## Rate of change of pressure

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
 Recognitions: Gold Member Science Advisor Staff Emeritus The conservation of momentum does not apply at all. Perhaps you should tell us the entire problem you're trying to solve? - Warren
 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

## Rate of change of pressure

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?
 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
 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?