A diffuser for an incompressible, inviscid fluid of density ? = 1000 kg/m3 consists of a diverging section of pipe. At the inlet, the diameter of the pipe is Di = 0.25 m, and at the outlet the diameter is Do = 0.75 m. The diffuser is 1 m long, and the diameter increases linearly with the distance x along the length of the diffuser. The velocity at the inlet of the diffuser is given by Vi = 5 m/s.
(i) Derive and plot the acceleration of a fluid particle through the diffuser, assuming uniform flow at each section.
(ii) Plot the pressure gradient through the diffuser, and find its maximum value.
(iii) If the pressure gradient must not be greater than 25 kPa/m, what must be the length of the diffuser ?