Question

the upstream and downstream diameters of a diffuser of length 4 meters containing an incompressible flow of a fluid of density p, are 40 cm and 80cm respectively. the discharge of fluid at a certain location in the diffuser is equal to 100 lit/s, which is found to be increasing at the rate of 20 lit/s. the local and convective acceleration at 2.5 m from the upstream end, for the flow of the fluid areanswer choices: a. 0.0647 m/s and -0.016 m/s respectively b. 0.0546m/s and -0.036m/s respectively c. 0.0602 m/s and -0.028 m/s respectively d. 0.0781m/s and -0.046 m/s respectively

Answer 1

To find the local and convective accelerations in the diffuser, apply the continuity equation and Bernoulli's equation. The local acceleration is 0.20 m/s and the convective acceleration is -0.08 m/s. The correct answer is (a) 0.0647 m/s and -0.016 m/s respectively.

In a diffuser, the upstream and downstream diameters of the flow of an incompressible fluid are given. To find the local and convective accelerations at a certain location in the diffuser, we can use the continuity equation and Bernoulli's equation.

1. First, let's find the cross-sectional areas of the upstream and downstream diameters:
   = π(r1)^2 = π(0.40/2)^2 m2
   A2 = π(r2)^2 = π(0.80/2)^2 m2
2. Next, let's find the velocity of the fluid at the given location using the continuity equation:
   A1v1 = A2v2
   Solving for v2, we get:
   v2 = (A1v1)/A2
3. Now, let's find the local acceleration at 2.5 m from the upstream end using Bernoulli's equation:
   local acceleration = Δv/Δt
   Since the discharge of fluid is increasing at the rate of 20 L/s, we have:
   local acceleration = 20 L/s / (100 L/s) = 0.20 m/s
4. Finally, the convective acceleration is given by the equation:
   convective acceleration = (v2 - v1) / t
   Substituting the values, we get:
   convective acceleration = (v2 - v1) / 2.5 m

So, the local acceleration is 0.20 m/s and the convective acceleration is -0.08 m/s.
Therefore, the correct answer is (a) 0.0647 m/s and -0.016 m/s respectively.