# Useful Formulae

38 LIQUIDSANDGASSES temperature, pressure and flow Liquid flowing at velocity v though a pipe with a crosssectional area Ahas a rate of flow qwhere q Av. Liquid flowing through two pipes of crosssectional areas A1 and A2, both subjected to the same pressure,will have flow velocities v1 and v2 ,whereA1v1 A2v2 . Pascals Principlestates that pressure applied to an enclosed liquid of any shape is transmitted evenly throughout,where pressure is defined as force per unit area. In the example illustrated opposite, F1A2 F2A1. Bernoullis Equationstates that a change of height results in a pressure change in a liquid p1 h1gp2 h2g lower opposite. Turning to gases,the Perfect Gas Lawstates that if a fixed quantity of gas has pressure P, volume V, andtemperature T in degrees Kelvin,thenPVis proportional to T. The Kelvin scale is a measure of absolute temperature,where K C 273. Given a closed system with initial pressure, volume and temperature P1 ,V1 and T1 ,and later values P2 ,V2 and T2 , CharlesLawstates for a constant pressure. Boyles Lawstates P1V1 P2V2 for a constant temperature. T 1 T2 V1 V2 39