Suppose you have a some volume, $V$, which contains a liquid, boiling off at a constant rate producing a constant gas flow, $f$, through an exhaust pipe of diameter, $d$. Is there a way of relating the diameter of the exhaust pipe to the pressure, $P$, of the volume?
I.e. by changing $d$ I should obviously see a change in $P$
I am looking at the Bernoulli equation, but i'm not sure if this is the correct approach? Are there any relations I can use?
Thanks!
Bernoulli is a reasonable approach so long as the gas flow is reasonably 'gentle' (no vortices or compression). However, to compare two cross sections of the exhaust then you need to average across the cross sections, yielding $$ \frac{v_1^2} {2} + \frac{p_1} {\rho} + \frac{1} {A_1} \int_{A_1} gz dA = \frac{v_2^2} {2} + \frac{p_2} {\rho} + \frac{1} {A_2} \int_{A_2} gz dA $$ The gravity term depends on the orientation and shape of the exhaust, but can probably be ignored to this level of approximation for a gas.
