9 An ideal fluid flows between the inclined walls of a two- dimensional channel into a sink tocat...
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Let F(x, y) be a two-dimensional vector field. Spose further that there exists a scalar function, o, such that Then, F(x,y) is called a gradient field, and φ s called a potential function. Ideal Fluid Flow Let F represent the two-dimensional velocity field of an inviscid fluid that is incompressible, ie. . F-0 (or divergence-free). F can be represented by (1), where ф is called the velocity potential-show that o is harmonic....
A fluid flows in an infinitely wide channel of height 2ℎ. The flow is steady, incompressible and laminar. A constant heat flux of magnitude q"w is applied on both walls. a. Derive the governing equation for the temperature distribution in the section of the channel where both velocity and temperature profiles are fully developed. b. Find the temperature distribution .c. Using the temperature distribution calculate the Nusselt number.
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an expression for the velocity potential ofa sink of strength (-m) placed at the origin of a two dimensional coordinate system in terms of r and ro, where ro is the radius of the equipotential = 0, sketch the pattern of the resulting equpotential lines. talce ongle r-S The flow field in a two dimentional incompressible flow has the horize omponent "u" and the vertical velocity component* derive (7 marks) 2
an expression for the velocity potential ofa sink...
2. The velocity potential for a spiral vortex flow is given by φ-2nInr-2-9, where A (positive) is the sink strength and Γ is the vortex strength (1) Find the expression of stream function. (2) The plot of stream function is shown in the following figure. Prove the angle,a, between the 2Tt velocity vector and the radial direction is constant throughout the flow field. (FYI, this spiral is called Logarithmic spiral.) .y
fluid mechanics
A steady, incompressible, and laminar flow of a fluid of viscosity u flows through an inclined narrow gap of a crack in the wall of length L and a constant width W shown in Figure Q1(b). Assume that the gap has a constant thickness of 7. The fluid flows down the inclined gap at an angle and in the positive x-direction. No pressure gradient is applied throughout the flow but there is gravitational effect. Derive an expression for...
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Z=x+ly Ideal potential flow field with velocity vector in 2- dimensional virtual (x, y) plane Complex potential function of a fluid flowing through a range with a volumetric flow m and F(2) = aperture range is given with. Where In; natural logarithmic function and sinh; sinus is hyperbolic function abbreviation, m and b are constant. Find the velocity components in Cartesian coordinates for this flow area in (sinh (5)
The Navier-Stokes equations are a system of non-linear, partial-differential equations that describe fluid flows. In the incompressible limit, the density of the fluid may be regarded as a constant, and the system of equations becomes, Because of the non-linearities, there are very few exact solutions that are known for these equations. One of the exact solutions is pressure-driven channel (or pipe) flow, also known as Poiseuille flow. In this flow, all solid, no-slip walls are parallel to the x-axis, and...
Question 2 Figure 2: Flow between two inclined plates Consider a two-dimensional plates, as shown in figure 2. Assume that pressure increases 30°. Acceleration due t o Pa and the channel height is h 10 cm inclined at te the velocity profile of the flow. State your assumptions and show your work. onal Newtonian, steady state, incompressible flow of a fluid be- by 1 kPa/ a dynamic viscosity of H1-1 x 10 amic viscosity of uo wall towards the right....
The stream function for a given two-dimensional flow field is w = 11x²y- (11/3)y3 Determine the corresponding velocity potential. Denote the constant of integration C. 4- (11x) ' - ( 11x) +C Edie
Question: 1115 Marks Consider a steady, two-dimensional, incompressible flow field called a source strength Q. Generate an expression for the stream function for this flow. (S Marks) a. , with flow b. Potential flow against a flat plate (Fig. 1a) can be described with the stream function where A is a constant. This type of flow is commonly called a stagnation point flow since it can be used to describe the flow in the vicinity of the stagnation point at...