A nozzle for an incompressible, inviscid fluid of density \(ho=1000 \mathrm{~kg} / \mathrm{m}^{3}\) consists of a horizontal converging section of pipe. At the inlet the diameter is \(D_{i}=100 \mathrm{~mm}\), and at the outlet the diameter is \(D_{o}=20 \mathrm{~mm}\). The nozzle length is \(L=500 \mathrm{~mm}\), and the diameter 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 \(V_{i}=1 \mathrm{~m} / \mathrm{s}\). Plot the pressure gradient through the nozzle, and find its maximum absolute value. If the pressure gradient must be no greater than \(5 \mathrm{MPa} / \mathrm{m}\) in absolute value, how long would the nozzle have to be?