Differential pumping

Differential pumping

Problem:

The governing equation of the problem is the following:
P2=G/S (1)
C(P1-P2)=P2S (2)

Note that P1>>P2, so the equation (2) can be written as
CP1=P2S.

In fact, if we believe these equation are true, the quantity P1 is not affected by the pumping speed Sas long as G is kept constant and P1>>P2. So changing the speed of the pump (e.g. by closing the gate valve upstream of pump to some extend) does not affect the pressure P1, at lest to the first order.

On the other hand, if all the quantities except P2are unknown, there is not way to know the pressure P1.