The Betz limit represents the maximum energy obtainable from a flowing fluid. This is a new topic for me, but Wikipedia has an entry under Betz' Law (don't forget the apostrophe after Betz) which may help you. This is a rather specialised topic and if Wikipedia does not give what you want you will probably have to consult a textbook on the subject.
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If we use the following form of the Van der Waals equation:(P+a/v2)(v - b) = RTwhereP is the absolute pressurev = system Volume/number of moles (i.e. V/n)R is the gas constant (aka universal gas constant or "Rankine constant")T is the absolute pressurea and b are Van der Waals constants for a particular gasThen we can solve for P as follows:(P+a/v2) = RT/(v - b)P = RT/(v - b) - a/v2If you want to solve for specific volume with respect to pressure, then you must do so at constant temperature.(P+a/v2)(v - b) = RT(P+a/v2)(v - b)v2= RTv2(Pv2+a)(v - b) = RTv2Pv3- Pbv2+ av - ab = RTv2Pv3- (Pb + RT)v2+ av - ab = 0We now have a polynomial equation of state which is cubic for the variable v.There is actually ananalytical solution for a cubic equation but it is a little bit complicated. Refer to the related link for the solution. Think of it as a cubic equationAv3+ Bv2+ Cv + D = 0whereA = PB = -Pb - RTC = aD = -abNote that v is a function of BOTH pressure and temperature.We can differentiate with respect to pressure and solve for dv/dP, but the equation is a little messy and requires solving the cubic equation to get the roots. If you want it, please rephrase the question to ask specifically for the formula for dv/dP.
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( | V1 - V2 | / ((V1 + V2)/2) ) * 100
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The equations of motion that relate velocity, distance, time and acceleration for the specific case of "constant acceleration" can be written as follow, acceleration a = (v2 - v1)/t from which v2 = v1 + at The distance covered during t time d = vav x t, where vav refers to average velocity in the process from v1 to v2. For the case of constant acceleration vav = (v1 + v2)/2. Substituting in d we get d = (v1 + v2)/2 x t from which, v2 = 2d/t - v1 If we take the constant acceleration to be zero, a = 0, you can see that the second equation we wrote becomes, v2 = v1 (There is no acceleration), so our equation for the distance d becomes, d = v1 x t = v2 x t