I have a quick question regarding compressible fluid flow, specifically: for a given amount of time, how much pressure is lost when attaching a balloon valve to a small air tank. I decided to model my solution after the following problem (from an old fluid mechanics text book of mine),(adsbygoogle = window.adsbygoogle || []).push({});

Air is extracted from a large tank in which the temperature and pressure are 70C and 101 kPa (abs), respectively, through a nozzle. At one location in the nozzle the static pressure is 25 kPa and the diameter is 15 cm. What is the mass flow rate? Assume isentropic flow.

and have solved up to the mass flow rate for my case (with the exception of rho). From here I would like to convert from my current mass flow rate to mass loss and eventually to pressure loss. I have assumed that: my case is a compressible fluid flow problem, the air contained within the tank can be considered an ideal gas, flow is isentropic (my analysis needs only to be a general estimate of the pressure lost), and standard temperature and pressure.

My original plan was to calculate the volumetric flow rate of the tank Q=V*A=(velocity*area)=dv/dt=(change in volume/change in time), integrate with respect to time and solve for the change in volume, then use p=nRT/v to find the pressure change. However, after some post-solving analysis, I came to the conclusion that, for my case, the volume is constant (seeing as how a tank will not expand under the pressures I am considering) and therefore my solution is not correct. I have so far solved for the velocity and area of the mass flow rate m_dot=rho*V*A, but unsure of how to proceed. Am I safe in using the density of air within the tank (standard temperature inside and outside the tank, standard atmospheric pressure outside the tank and 200 psi inside the tank) for my calculation of the mass flow rate. Moreover, how should I continue from here (total mass of air lost) to the total pressure loss during attachment? Thank you for your time.

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# Compressible Fluid Flow

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