Revised design of an air duct (Fig. 7B.5), a straight, horizontal air duct was to be installed in a factory. The duct was supposed to be 4 ft x 4 ft in cross section. Because of an obstruction, the duct may be only 2 ft high, but it may have any width. How wide should the duct be to have the same terminal pressures and same volume rate of flow? Assume that the flow is turbulent and that the Blasius formula (Eq. 6.2-12) is satisfactory for this calculation. Air can be regarded as incompressible in this situation. 

(a) Write the simplified versions of the mechanical energy balance for ducts I and II. 

(b) Equate the pressure drops for the two ducts and obtain an equation relating the widths and heights of the two ducts. 

(c) Solve the equation in (b) numerically to find the width that should be used for duct II.

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H - 4 ft Pump Duct I W, = 4 ft P2 H =2 ft Pump Duct II W= ? ft P2 Pij Plane 1 Plane 2