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Consider steady, incompressible, laminar flow of a Newtonian fluid in an infinitely lons round pipe annulus of inner radius
FIGURE P9-98
the x-axis, and
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EBK FLUID MECHANICS: FUNDAMENTALS AND A
- A frictionless, incompressible steady flow field is given byV = 2xyi - y2jin arbitrary units. Let the density be ρ 0 = constant andneglect gravity. Find an expression for the pressure gradientin the x direction.arrow_forwardA potential steady and incompressible air flow on x-y plane has velocity in y-direction v= - 6 xy . Determine the velocity in x-direction u=? and Stream Function SF=? ( x2 : square of x ; x3: third power of x ; y2: square of y , y3: third power of y)ANSWER: u= 3 x2 - 3 y2 SF= 3 x2 y - y3arrow_forwardHello sir Muttalibi is a step solution in detailing mathematics the same as an existing step solution EXAMPLE 6-1 Momentum-Flux Correction Factor for Laminar Pipe Flow CV Vavg Consider laminar flow through a very long straight section of round pipe. It is shown in Chap. 8 that the velocity profile through a cross-sectional area of the pipe is parabolic (Fig. 6-15), with the axial velocity component given by r4 V R V = 2V 1 avg R2 (1) where R is the radius of the inner wall of the pipe and Vavg is the average velocity. Calculate the momentum-flux correction factor through a cross sec- tion of the pipe for the case in which the pipe flow represents an outlet of the control volume, as sketched in Fig. 6-15. Assumptions 1 The flow is incompressible and steady. 2 The control volume slices through the pipe normal to the pipe axis, as sketched in Fig. 6-15. Analysis We substitute the given velocity profile for V in Eq. 6-24 and inte- grate, noting that dA, = 2ar dr, FIGURE 6–15 %3D Velocity…arrow_forward
- Velocity components in the flow of an ideal fluid in a horizontal plane; Given as u = 16 y - 12 x , v = 12 y - 9 x a) Is the current continuous?(YES OR NO) b) Can the potential function be defined?(YES OR NO) c) Find the unit width flow passing between the origin and the point A(2,4). (y(0,0)=0) d) Calculate the pressure difference between the origin and the point B(3;3).arrow_forwardA capillary tube has an 8mm inside diameter through which liquid fluorine refrigerant R-11 flows at a rate of 0.03 cm3/s. The tube isto be used as a throttling device in an air conditioning unit. A model of this flow is constructed by using a pipe of 3cm inside diameter and water as the fluid medium. (Density of R-11 = 1.494 g/cm3 and its viscosity is 4.2 x10-4 Pa.s; Density of water is 1g/cm3 and its viscosity 8.9 x10-4 Pa.s)a) What is the required velocity in the model for dynamic similarity? Hint: For flow through a tube the Ne number can be expressed in terms of the Reynolds numberb) When dynamic similarity is achieved the pressure drop is measured at 50 Pa. What is the corresponding pressure drop in the capillary tube?Hint: In this case the Euler number defines dynamic similarity with reference to the static pressure droparrow_forwardConsider a two-dimensional flow which varies in time and is defined by the velocity field, u = 1 and v = 2yt. Is the flow field incompressible at all 9mes?arrow_forward
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- SAE-10 oil at 20 deg C fills the gap between the moving 6 cm diameter long cylinder which is inside a fixed outer cylinder 6.8 cm diameter. Calculate the pressure gradient per unit length needed so the shear stress on the outer cylinder is exactly equal to zero when the inner cylinder is moving with velocity V=4 m/s in the negative z-direction. Assume laminar flow. The viscosity of the oil is 99.2 cp. Express your result in kPa/m and round your numerical answer to a whole numberarrow_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_forwardConsider steady, incompressible, parallel, laminar flow of a viscous fluid falling between two infinite vertical walls. The distance between the walls is h, and gravity acts in the negative z-direction (downward in the figure). There is no applied (forced) pressure driving the flow—the fluid falls by gravity alone. The pressure is constant everywhere in the flow field. For the fluid falling between two parallel vertical walls, generate an expression for the volume flow rate per unit width (V·/L) as a function of ?, ? , h, and g. Compare your result to that of the same fluid falling along one vertical wall with a free surface replacing the second wall, all else being equal. Discuss the differences and provide a physical explanation.arrow_forward
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