## Integrating equations in python

Posted January 20, 2013 at 09:00 AM | categories: integration, python | tags:

Updated February 27, 2013 at 02:54 PM

A common need in engineering calculations is to integrate an equation over some range to determine the total change. For example, say we know the volumetric flow changes with time according to \(d\nu/dt = \alpha t\), where \(\alpha = 1\) L/min and we want to know how much liquid flows into a tank over 10 minutes if the volumetric flowrate is \(\nu_0 = 5\) L/min at \(t=0\). The answer to that question is the value of this integral: \(V = \int_0^{10} \nu_0 + \alpha t dt\).

import scipy from scipy.integrate import quad nu0 = 5 # L/min alpha = 1.0 # L/min def integrand(t): return nu0 + alpha * t t0 = 0.0 tfinal = 10.0 V, estimated_error = quad(integrand, t0, tfinal) print('{0:1.2f} L flowed into the tank over 10 minutes'.format(V))

100.00 L flowed into the tank over 10 minutes

That is all there is too it!

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