By C. A. Brebbia and A. J. Ferrante (Auth.)

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7 Applications of the momentum equation In many cases the momentum equation is used in combination with the continuity equation and Bernouilli's equation to study complex flow problems. It can be used in problems for which there is a sudden change in velocity or flow direction, as in hydraulic pumps, hydraulic machineries, etc. 1 Nozzle Assume that we have a nozzle in a tube, which produces a water jet discharging in the atmosphere. In such a case one needs to know the reaction force R produced by the contraction.

Calculate the pressure at the stagnation point in the front of the submarine. Assume that the point is situated 20 m below sea level. 28 Dimensionless numbers 43 rate of flow Q assuming that Dx = 30 mm, D2 = 10 mm, hm = 12 mm, pm is the density of mercury and p is the density of water at 20°C. 040 N s m~ 2 , flowing in a 100 mm diameter pipe at a rate of 5 litres" 1 . 28. Assume that the discharge Q is 50 m 3 s " * and the total loss of head due to friction in the pipe, turbine, etc. is 10 m. Calculate the power produced by the turbine.

In standard water networks, pressures are of the order of 20 to 60 N c m - 2 . 5 cm diameter. 5 m for a 500 m pipe. They could become larger, however, for pipes of smaller diameters. The analysis of pipe networks is normally done using computer programs. 1. The pipe sizes, the geometric dimensions of the network, and the consumptions at the nodes constitute the data. The system has to be solved for the energy heads at each of the nodes, and the discharges at each of the pipes, which are the unknowns.

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