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Consider steady flow of water through an axisymmetric garden hose nozzle (Fig. 9-28). Suppose the axial component of velocity increases linearly from
FIGURE P9-28
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Fluid Mechanics: Fundamentals and Applications
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- Consider a steady, two-dimensional, incompressible velocity field with u = ax + b and ? = −ay + cx, where a, b, and c are constants: a = 0.50 s−1, b = 1.5 m/s, and c = 0.35 s−1. Generate an expression for the stream function and plot some streamlines of the flow in the upper-right quadrant.arrow_forwardFind the two-dimensional velocity potential ϕ ( r , θ ) for thepolar coordinate fl ow pattern υ r = Q / r , υ θ = K / r , where Qand K are constants.arrow_forwardConverging duct flow is modeled by the steady, twodimensional velocity field V-›= (u, ? ) = (U0 + bx) i-›− byj-› where U0 is the horizontal speed at x = 0 . As vertical line segment AB moves downstream it shrinks from length ? to length ? +Δ? assketchedin.Generateananalytical expression for the change in length of the line segment, Δ? . Note that the change in length, Δ? , is negative.arrow_forward
- The flow of an incompressible §uid is defined by u=3, v=9x. Does a stream function exist for this flow? If so, determine the expression for the stream function,Ψ.arrow_forwardConsider a uniform stream of magnitude V inclined at angle ?. Assuming incompressible planar irrotational flow, find the velocity potential function and the stream function. Show all your work.arrow_forwardIn a certain two‐dimensional flow field, the velocity is constant with components u = –4 ft/s and v = –2 ft/s.Determine the corresponding stream function and velocity potential for this flow field. Sketch theequipotential line φ = 0 which passes through the origin of the coordinate system. Could you answer and explain every step pleasearrow_forward
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