6.60 Potential flow against a flat plate (Fig. P6.60a) can be de- scribed with the stream function ý = Axy where A is a constant. This type of flow is commonly called a “stag- nation point" flow since it can be used to describe the flow in the vicinity of the stagnation point at O. By adding a source of strength m at O, stagnation point flow against a flat plate with a “bump" is ob- tained as illustrated in Fig. P6.60b. Determine the relationship be- tween the bump height, h, the constant, A, and the source strength, m. (a) Source (b) IFIGURE P6.60

6.60 Potential flow against a flat plate (Fig. P6.60a) can be de- scribed with the stream function ý = Axy where A is a constant. This type of flow is commonly called a “stag- nation point" flow since it can be used to describe the flow in the vicinity of the stagnation point at O. By adding a source of strength m at O, stagnation point flow against a flat plate with a “bump" is ob- tained as illustrated in Fig. P6.60b. Determine the relationship be- tween the bump height, h, the constant, A, and the source strength, m. (a) Source (b) IFIGURE P6.60

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Assume an inviscid, incompressible flow. Also, standard sea level density and pressure are 1.23 kg/m3 (0.002377 slug/ft3) and 1.01 × 105 N/m2 (2116 lb/ft2), respectively. Derive the velocity potential for a doublet.
Water at 20 ° C flows steadily through the piping junction inFig. P3.32, entering section 1 at 20 gal/min. The averagevelocity at section 2 is 2.5 m/s. A portion of the flow isdiverted through the showerhead, which contains 100 holesof 1-mm diameter. Assuming uniform shower flow, estimatethe exit velocity from the showerhead jets.
Complete solution and Readable
Q.3 The velocity components in the x and y directions of a two dimensional is equal to potential flow are u and v, respectively. Then (a) (b) ax (c) (d) ay
SAE 10 oil at 20 °C flows through the 4-cm-diameter verticalpipe of Fig. P6.30. For the mercury, manometer readingh = 42 cm shown, (a) calculate the volume flow rate inm3/h and (b) state the direction of flow.
Q.4 A steady, uniform-density, 2-D flow is to be calculated on the square grid shown below. The boundary velocities are given as; v₁ =30, V = 40,uc=100, u = 50, u = 200, u, = 210, V = 0 and v₁ = 20. Among these numbers, there is some doubt about correctness of the value of u,. If all other numbers are correct, what should be the correct value of u,? The internal velocities are governed by simplified momentum equations given by: up = 70+0.5 (P₁-P₂) u, = 10 +0.7 (P3-P4) V =30+0.5(P3-P₁) VG =18+0.8(P₁-P₂) Write discretized continuity equation for each control volume. Derive the discretization equation for pressure by substituting from momentum equations, following SIMPLER calculation procedure. Solve the pressure equations to obtain P₁, P2, P3 and P₁. Hence obtain values of up, u, V and VG
SAE 50W oil at 20 °C flows from one tank to anotherthrough a tube 160 cm long and 5 cm in diameter. Estimatethe flow rate in m3/hr if z1 = 2 m and z2= 0.8 m.
5. The stream function for a two-dimensional incompressible flow is ax? ay2 + bxy 2 Where a, and b are known constants. Find the velocity potential for the flow.
Q4) Water at 40°C flows horizontally through a constriction similar to that in Fig. S5.9 when the atmospheric pressure is 715 mmHg. The gage reading is 35 kPa, d, =0.5 m, and d, =0.15 m. Neglecting head loss, find the flow rate at which cavitation begins. O 10 psi Throat 1 ft dia Table A.1 at 40°C: y = 9.731 kN/m³ , 3 ft dia Figure S5.9
1. Obtain Bernoulli’s equation for compressible flow considering adiabatic process. 2, Define vortex flow. Derive an expression of stream function and velocity potential function for vortex flow. 3. What is Venturi meter? Derive an expression for discharge through venturi meter. 4. What is Venturi meter? Derive an expression for discharge through venturi meter.
Water flows through a two-dimensional narrowing wedgeat 9.96 gal/min per meter of width into the paper(Fig. P4.72). If this inward flow is purely radial, find anexpression, in SI units, for ( a ) the stream function and( b ) the velocity potential of the flow. Assume onedimensionalflow. The included angle of the wedge is 45 ° .
6.6 The boundary layer thickness d at any section for a flow past a flat plate de- pends upon the distance x measured along the plate from the leading edge to the section, free stream velocity U and the kinematic viscosity v of the fluid. Show with the help of Rayleigh's indicial method of dimensional analysis that c (Ux/v) or %3D