Problem: Water decelerates in a diffuser following the relation 𝑉=𝑉𝑜(1−𝐴𝑥2𝐿2) where x is the distance from the start of the diffuser. At time = 0, the flow to the diffuser is turned off slowly and the inlet velocity V0 decays with time as 𝑉𝑜=𝑉𝑖𝑒−𝑏𝑡. The velocity Vi = 50 ft/s, A = 0.1, L = 2 ft, and b = 0.1s-1. The flow can be treated as one-dimensional.
1. Determine the local and convective acceleration at time = 0 and 5 s at both the entrance and the exit.
2. Determine the acceleration of the fluid at time = 0 and 5 s at both the entrance and the exit.
3. Examine* the convective acceleration term if the inlet velocity decayed more rapidly?