Question

MIT Marine Hydrodynamics Spring 2005 Problem Set 5B

Please solve these for me thanks ! :)

1. Supplementary Problem 12 2. A fluid jet issues from a long vertical slot and strikes against a vertical flat plate at an angle. The resulting two-dimensional steady flow in a horizontal plane is shown below. The plate is frictionless (a) If the volume flow rate of a vertical section of the jet before it strikes the plate is Q A, where A, is the section area, find the flow rates Q and Q, in terms of Q, (Hint: think Bernoulli) (b) Find the magnitude of the force F exerted on the vertical section of the plate. V Hint: Consider a coordinate system that makes momentum analysis easy 3. Complete the following statements equation (a) The vorticity equation is derived from the (b) In the case of inviscid flow, the time rate of change of vorticity following a fluid particle depends on vortex in turn depend on the velocity gradients at the particle's location _ and vortex , which (c) The Bernoulli equation for steady, ideal flow is not valid for potential flow (TRUE or FALSE 12. Consider the three-dimensional inviscid incompressible flow with velocity components given by: u(x, y, z, t)-A(t)y - Ba v(xr, y, z, t) A(t)x - By w(r, y, z, t) w(z) (a) Find w(z) given w(0) = 0. (b) Describe this flow in words and/or pictures (e) Determine the vorticity vector. (d) Find the function A(t) from the vorticity equation given A(0) = 1. (e) Find the circulation '(t) around a path of fluid particles initially (i.e. at t = 0) located in a circle of radius 1 on the plane z = 1

Answer 1

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