State if the flow represented by u = 3x + 4y and v= 2x – 3y is rotational or irrotational. [Ans. Rotational]
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- A sink of strength 20 m2/s is situated 3 m upstream of a source of 40 m²/s in a uniform stream. It is found that, at a point 2.5 m from both source and sink, the local velocity is normal to the line joining the source and sink. Find the velocity at this point and the velocity of the uniform stream. Locate any stagnation points and sketch the flow field.A Rankine half-body is formed as shown in Fig. . Forthe stream velocity and body dimension shown, compute(a) the source strength m in m2/s, (b) the distance a, (c) thedistance h, and (d) the total velocity at point A.6 For incompressible flow, density remains the same Select one: True False
- Please indicate the given, assumption and illustration. A source with strength 0.25 m2/s and a vortex with strength 1 m2/s (counter-clockwise) are located at the origin. After working out the equations for the stream function and velocity potential components, determine the following velocity components at a point P(1, 0.5): A) The Radial Velocity component in meters/second. B) The Tangential Velocity Component in meters/second.for the following flows, find the equation of the streamline through(1,1). v= -y^(2)i-6xjQ2: The linear-scale ratio 1:30 of open-channel model, the velocity and flow rate are 1.5 m / s and 2 m / s. Determine the corresponding velocity and flow rate in the prototype.
- A two-dimensional flow field has an x-component of velocity given in Cartesian coordinates by u = 2x − 3y. (a) Find v, the y-component of velocity, if the flow is incompressible and v = 0 when x = 0. (b) If the flow follows the Bernoulli equation, find an expression for the pressure distribution as a function of x and y, given that the pressure is p0 at the stagnation point.Homework! Parts A-C and label them Question: A two-dimensional incompressible flow has the velocity components u = 5y and v = 4x. Part A - Check continuity equation is satisfied. Part B - Are the Navier-Stokes equations valid? Part C - If so, determine p(x,y) if the pressure at the origin is po. HINT *** : u = 5y and v = 4x.Plot the streamlines and potential lines of the fl ow due to aline source of strength m at (a, 0) plus a source 3m at(2a, 0). What is the fl ow pattern viewed from afar?
- In two dimensions along the converging nozzle, stable, considering incompressible flow. The velocity on the horizontal centerline (x-axis) is given as V=V1(1+x/L)i Derive an equation for the acceleration of a particle moving along the centerline using (a) Euler's approximation and (b) Lagrangian approximation. Discuss the acceleration for the particle being at the beginning and end of the channel.If the vorticity in a region of the flow is zero, the flow is (a) Motionless (b) Incompressible (c) Compressible (d ) Irrotational (e) RotationalUse the case V(u,v)=(8−ax)i^+(4−b^2y)j^ to evaluate the magnitude of velocity and acceleration at a coordinate point (5,5) in terms of the constants a and b. State the acceleration vector. Under what conditions is this flow field satisfying the conservation of mass of an incompressible flow?