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By means of the mechanical quadrature, the author mathematically derives the reasonable positions of the velocity-measuring points, where the Pitot-tubes may be inserted, along a diameter in a cross section of a circular pipe, together with his new formulas for calculating the discharge rate. These formulas may be satisfactorily applied to a flow whose velocity distribution along any diameter of the cross section is as approximately equal as is required in the ordinary method. There are three different types of these new formulas according to the different ways of their derivation. However, it is theoretically shown that any one of these formulas gives more accurate results than the ordinary formula.

THE DERIVATION OF THE FORMULAS FOR CALCULATING THE DISCHARGE RATE IN A PIPE, BY MEANS OF THE MECHANICAL QUADRATURE