Which of these represent time averaging?(a) \(\frac{1}{V}\int_V \phi dV\)(b) \(lim_{V→∞}\frac{⁡1}{V}\int_V \phi dV\)(c) \(\frac{1}{T}\int_t^{t+T}\phi dt\)(d) \(lim_{T→∞}⁡\frac{1}{T}\int_t^{t+T}\phi dt\)This question was posed to me in homework.Enquiry is from Turbulence Modelling in portion Turbulence Modelling of Computational Fluid Dynamics

Which of these represent time averaging?(a) \(\frac{1}{V}\int_V \phi d

1.	Which of these represent time averaging?(a) \(\frac{1}{V}\int_V \phi dV\)(b) \(lim_{V→∞}\frac{⁡1}{V}\int_V \phi dV\)(c) \(\frac{1}{T}\int_t^{t+T}\phi dt\)(d) \(lim_{T→∞}⁡\frac{1}{T}\int_t^{t+T}\phi dt\)This question was posed to me in homework.Enquiry is from Turbulence Modelling in portion Turbulence Modelling of Computational Fluid Dynamics
Answer» The correct answer is (d) \(lim_{T→∞}⁡\frac{1}{T}\int_t^{t+T}\phi DT\) Best EXPLANATION: Time averaging represents the average of the flow variable BASED on a time interval ‘T’. It USES INTEGRATION to sum up the flow variables at different times and then divides by the time interval \(lim_{T→∞}⁡\frac{1}{T}\int_t^{t+T}\phi dt\).

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