Find the location of the stagnation point for the flow due to a vortex +I at (2a, 0) and a vortex -25 at (-2a, 0).

6.4 The three components of velocity in a flow field are given by u = x² + v² + z² v = xy + yz + z? w = -3xz – z2/2 + 4 Determine an expression for the rotation vector. Is this an irrotational flow field?

The streamlines in a particular two-dimensional flow field are all concentric circles, as shown in Fig. 5 the equation v, = wr where w is the angular velocity of the rotating mass of fluid. Determine the circulation around the path ABCD. The velocity is given by B Figure 5

A jet of air having velocity V₁ and cross-sectional area A₁ strikes an inclined plate as shown in the figure. Neglect any effects of viscosity. V₁ (a) Find V₂ and V3 in terms of V₁. Note that the pressure is patm everywhere. (b) Because viscous effects are negligible, there is no way for the air to exert a force on the plate in the tangential (z) direction. Using the coordinate system in the figure, find A₂ and A3 in terms of A₁ and 0. (c) For V₁ = 50 m/s, A₁ = 5 x 10-4 m², and 0 = 60°, find the force required to hold the plate in place. Neglect the weight of the plate. Recall that pair = 1.225 kg/m³.

Compare free vortex with forced vortex according to velocity and static pressure distribution. Think motion into hole of water in a bathtub. Discuss the reasons of formation of free vortex motions rotating in different directions in north and south hemisphere in the world while no rotation motion is seen at equatorial plane. Investigate similar physical phenomena in universe.

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.

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The tank of water shown below is 15 cm wide into the paper. The tank is accelerated in rigid- body motion at 9 m/s² in x-direction (right) and 2 m/s“ in z-direction (upwards). Assume no spilling. (a) Show with sketch what will happen to surface point B. (b) Find the angle 0 and the new water depth (height) of side AB. (c) Calculate the water force on wall AB. 3 Given: Specific Weight of Water, Ywater = 9790 N/m', Draw sketch and show all calculations. B 20 cm Water at 20°C 36 cm