• Card 18 / 41: Recall that the tank filling problem in Subunit 3.4 resulted in an ordinary differential equation dh/dt A = Q - fh, where h is the height of fluid in the tank, Q is the volumetric flow rate in, H is the height of the tank, A is the cross sectional area of the tank, and f is a parameter with units of length2/time. We may write this equation in a dimensionless form d η dτ = 1 - (fH/Q) η, where η= h/H. Which of the following definitions of τ is consistent with the dimensionless equation?
    A) tQ/AH
    B) fH/Q
    C) tf/AQ
    D) fAQ/t

    Answer:
    A) tQ/AH

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Explanation:

One way forward is first to check whether each answer is dimensionless. Another way forward is to start with the differential equation and then divide each side by H/Q. Then group terms until you reach the form of the de/un/non-dimensionalized equation shown.

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Fluid Mechanics ME201

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Attribution:  Stephanie Redfern and Tuan Dinh. Fluid Mechanics. The Saylor Academy 2014, http://www.saylor.org/courses/me201/
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