I am doing some simple flow experiments and my instruments are giving me strange results - I think they are broken, I need a sanity check for my understanding of the flow in my system to confirm it.
Here is a schematic. An inlet has a gauge pressure of 19 inches of water gauge (19"wg). The stream gets split up into two, pipes A and B. Both pipes lead to the same atmospheric pressure (Pe = 0).
I have denoted the net resistance in the two lines with $R_A$ and $R_B$.
Here is what I am wondering about: Do $P_A$ and $P_B$ necessarily have to be equal to 19"wg? If I double the resistance RB, how will that affect the pressure PA? If RB doubles, then the resistance in line B will be more, diverting more flow into line A. That means the velocity in line A has suddenly increased (since RA did not change). According to Bernoulli then, the pressure PA has to drop. Is this correct?
The principle of continuity applies where $Q_{in} = Q_A + Q_B$ and the energy per unit mass according Bernoulli, i.e. $\frac{P_{in}}{\rho} + \frac{V_{in}^2}{2} = \frac{P_A}{\rho} + \frac{V_{A}^2}{2} = \frac{P_B}{\rho} + \frac{V_{B}^2}{2}$
I am trying to think about this intuitively with a sort of hydraulic analogy - in terms of resistors, pressures and flows ($\frac{P}{R} = Q$).