Consider Problem 6.16 with the diffuser 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 \(V_{i}=12 \mathrm{~m} / \mathrm{s}\). Plot the pressure gradient through the diffuser, and find its maximum value. If the pressure gradient must be no greater than \(20 \mathrm{kPa} / \mathrm{m}\), how long would the diffuser have to be?

Data From Problem 6.16

6.16 A diffuser for an incompressible, inviscid fluid of density p = 1000 kg/m consists of a horizontal diverging section of pipe. At the inlet the diameter is D; = 0.25 m, and at the outlet the diameter is Do=0.75 m. The diffuser length is L = 1 m, and the diameter increases linearly with distance x along the diffuser. Derive and plot the accel- eration of a fluid particle, assuming uniform flow at each section, if the speed at the inlet is V = 5 m/s. Plot the pressure gradient through the diffuser, and find its maximum value. If the pressure gradient must be no greater than 25 kPa/m, how long would the diffuser have to be?