A diffuser for an incompressible, inviscid fluid of density \(ho=1000 \mathrm{~kg} / \mathrm{m}^{3}\) consists of a horizontal diverging section of pipe. At the inlet the diameter is \(D_{i}=0.25 \mathrm{~m}\), and at the outlet the diameter is \(D_{o}=0.75 \mathrm{~m}\). The diffuser length is \(L=1 \mathrm{~m}\), and the diameter increases linearly with distance \(x\) along the diffuser. Derive and plot the acceleration of a fluid particle, assuming uniform flow at each section, if the speed at the inlet is \(V_{i}=5 \mathrm{~m} / \mathrm{s}\). Plot the pressure gradient through the diffuser, and find its maximum value. If the pressure gradient must be no greater than \(25 \mathrm{kPa} / \mathrm{m}\), how long would the diffuser have to be?