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As the flow mass curve or runoff mass curve is the cumulative flow volume 'V' versus of time curve. The mass curve ordinate 'V' at any time t is:
(Where, Q = discharge)

  • A.\(V = \int_{0}^{T} Q^{2} \cdot dt\)
  • B.\(V = \int_{0}^{T} Q^{3} \cdot dt\)
  • C.\(V = \int_{0}^{T} Q \cdot dt\)
  • D.\(V = \int_{0}^{T} 1/Q \cdot dt\)

Answer: C

The mass curve ordinate is \(V = \int_{0}^{T} Q \cdot dt\).

The mass curve plots the cumulative volume of flow against time. The volume that passes in a short interval is \(Q\,dt\), so the cumulative volume from the start up to time T is the integral of the discharge:

\[ V = \int_{0}^{T} Q\, dt \]

Its slope at any point is therefore the discharge, \(dV/dt = Q\), which is how storage is found from it. Integrating \(Q^{2}\), \(Q^{3}\) or \(1/Q\) gives quantities without the dimensions of volume.

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