The rate of change of pressure (Urgent, )

[sarahh]

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.

Thank you very much for your kind assistance.

Sarah

 

[Aaron Barnard]

Yes, your explanation is accurate. The conservation of momentum law states that the rate of momentum change produced by an external force (the pump in this case) is equal to the rate of momentum change produced by the system. In other words, the rate at which momentum is lost or gained due to the pump is equal to the rate at which the system gains or loses momentum. This means that the rate of change of pressure due to the pump must be equal and opposite to the rate of change of pressure due to the system. Thus, your explanation is correct.

 

[M98Ranger]

Yes, it is accurate to explain this observation using the concept of conservation of momentum. The rate of change of pressure, dP1/dt, represents the rate at which momentum is being added to the system by the pump. However, after 3 minutes, the system has reached a state of equilibrium where the pressure difference, dP2, is equal and opposite to the pressure difference created by the pump. This means that the rate of momentum-changing force per unit area, -dP2/dt, is balancing out the rate of momentum-changing force produced by the pump, dP1/dt. This is in line with the principle of conservation of momentum, which states that in a closed system, the total momentum remains constant. Therefore, your explanation is accurate.