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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
- In the fig-Shown, the Flow rate Pipe (A) is equal ( QA= 25 Lit15), he diameter is equal ( DA = 75mm, Do 60mm, De = Dc =30 mm). and the velocity in Pipe (D) is equal ( 40=5m/s). the relation between flow rate in Pipe (B) and pipe (c) in %3D %3D PB =3 Qc. Find the Ualue of .. 2- UA, UB, Uc: Pe =30 mm water Pc = 30 mm imput QA = 25 2it/sec = 75 mm Po = 6omm input = A outPut = B, C, D accumu lation = o.arrow_forwardQI A/ The inviscid, steady, and incompressible 2D flows are given by (a) o =x- 3xy (b) y = x-2xy-y? In each case, find the components of velocity in x- and y-directions.arrow_forwardFluid Mechanics Question An incompressible fluid flows in the converged nozzle provided in the figure. nozzle area -> A=Ao*(1-b*x) entry speed -> V=Vo*(0.5+0.5*cos(w*t)) Vo:20m/s Ao=1.5 m2 L=13m b=0.2/22 W=0.16rad/s Find the acceleration in the nozzle center as a function of time * (to multiplication) / (to divide)arrow_forward
- b Water flows around the vertical two-dimensional bend with circular streamlines and constant velocity as shown in the figure below. If the pressure is 62 kPa at point (1), determine the pressures at points (a) (2) and (b) (3). Assume that the velocity profile is uniform as indicated. = Esc Type here to search L 1 A 30 @ 2 W S 4x F2 # 3 E 4₁ D O $ 4 R F F4 % 5 2m 99+ FS T G A 6 4 m 1 m Y H (3) (2) (1) * F7 & 7 V = 10 m/s U PrtScn FB 8 Home 9 K 9 End F10 ) 0 L 36°F Clear PgUp F11 P PgDn 40 + (1) 7:00 PM 11/21/2022 Del Backsparrow_forwardConsider steady, incompressible, two-dimensional flow through a converging duct (Figure below). Uo A simple approximate velocity field for this flow of the Converging duct flow is modeled by the steady, two- dimensional velocity field given by: V = (u, v) = (U, + bx)i – byj The pressure field is given by: P = P, – 2U,bx + b*(x² + y²) Where Po is the pressure at x = 0. Generate an expression for the rate of change of pressure following a fluid particle?arrow_forwardQuestion 3 (a) A two-dimensional flow velocity field in the domain with non-dimensional coordinates x > 0 and y > 0 is defined as: v = -Upxy i+ Upxy j where i and j are the unit vectors in the x- and y-directions respectively and Uo is a constant with units m/s. (i) Determine the magnitude and direction of the velocity at the point (1,1). (ii) Find the equation of the streamlines.arrow_forward
- Question 3 : A line source at y-axis is located 1 m above the horizontal plate (x-axis), where the flow rate per unit length is, m²/s.. (a) Using x, and, y, in m, write the stream function of the potential flow in both Cartesian and polar coordinates. (b) Express the radial component velocity in polar coordinates and hence find the velocity magnitude at, x = 0, and, y = 2. (c) Calculate the radial and angular component velocity at, x = 1, and, y 1, and hence find the velocity magnitude and direction. (d) If the source is placed near a corner where the distance from horizontal and vertical plate are 1 m, determine the stream function of the potential flow and find the velocity on the horizontal plate right below the source. =arrow_forward3. The two-dimensional velocity field in a fluid is given by V 2ri+ 3ytj. (i) Obtain a parametric = equation for the pathline of the particle that passed through (1.1) at t = 0. (ii) Without calculating any equation: if I were to draw the streak-line at t = 0 of all points that passed through (1, 1) would it be the same or different? Justify yourself.arrow_forwardAsaparrow_forward
- Q4: The velocity components for a two dimensional incompressible flow are u = - 6xy, v=-3x2 + 3y2 1) Is the flow satisfied the continuity equation?. 2) Obtain an expression of stream function 3) Obtain an expression for the velocity potential if it is exsits.arrow_forwardVelocity field of an incompressible flow is given by V = 6xi − 6yj (m/s) a) Find the pathlines in x-y plane. Make a sketch of pathlines for x ≥ 0 and y ≥ 0. b) Find the streamlines. Make a sketch of streamlines for x ≥ 0 and y ≥ 0. c) At time t = 0 s, the position of a rectangular fluid element ABCD is described by the corner points A(1,3), B(2,3), C(1,2) and D(2,2). Determine the new position of the fluid element at time t = 1/6 sarrow_forwardFind stream function and velocity potential.arrow_forward
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