Consider Problem 6.15 with the nozzle directed upward. Assuming that the flow is uniform at each section, derive and plot the acceleration of a fluid particle for an inlet speed of \(V_{i}=2 \mathrm{~m} / \mathrm{s}\). Plot the pressure gradient through the nozzle and find its maximum absolute value. If the pressure gradient must be no greater than \(7 \mathrm{MPa} / \mathrm{m}\) in absolute value, how long would the nozzle have to be?

Data From Problem 6.15

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6.15 A nozzle for an incompressible, inviscid fluid of density p=1000 kg/m consists of a horizontal converging section of pipe. At the inlet the diameter is D; = 100 mm, and at the outlet the diam- eter is Do = 20 mm. The nozzle length is L= 500 mm, and the diam- eter decreases linearly with distance x along the nozzle. Derive and plot the acceleration of a fluid particle, assuming uniform flow at each section, if the speed at the inlet is V; = 1 m/s. Plot the pressure gradient through the nozzle, and find its maximum absolute value. If the pressure gradient must be no greater than 5 MPa/m in absolute value, how long would the nozzle have to be?