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Consider the supersonic flow over a 5° half-angle wedge at zero angle of attack, as sketched in Figure 1.16a. The freestream Mach number ahead of the wedge is 2.0, and the freestream pressure and density are 1.01 × 10$ N/m² and 1.23 kg/m', respectively (this corresponds to standard sea level conditions). The pressures on the upper and lower surfaces of the wedge are constant with distance s and equal to each other, namely, pu = pi = 1.31 × 10° N/m², as shown in Figure 1.16b. The pressure exerted on the base of the wedge is equal to pœ. As seen in Figure 1.16c, the shear stress varies over both the upper and lower surfaces as r, = 431s-0.2. The chord length, c, of the wedge is 2 m. Calculate the drag coefficient for the wedge. 34.2 Wae ange

Consider the supersonic flow over a 5° half-angle wedge at zero angle of attack, as sketched in Figure 1.16a. The freestream Mach number ahead of the wedge is 2.0, and the freestream pressure and density are 1.01 × 10$ N/m² and 1.23 kg/m', respectively (this corresponds to standard sea level conditions). The pressures on the upper and lower surfaces of the wedge are constant with distance s and equal to each other, namely, pu = pi = 1.31 × 10° N/m², as shown in Figure 1.16b. The pressure exerted on the base of the wedge is equal to pœ. As seen in Figure 1.16c, the shear stress varies over both the upper and lower surfaces as r, = 431s-0.2. The chord length, c, of the wedge is 2 m. Calculate the drag coefficient for the wedge. 34.2 Wae ange

Elements Of Electromagnetics
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
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Find the A', N', L', D'

**Example: Supersonic Wedge** **Problem Statement:** Consider the supersonic flow over a 5° half-angle wedge at zero angle of attack, as sketched in Figure 1.16a. The freestream Mach number ahead of the wedge is 2.0, and the freestream pressure and density are 1.01 × 10⁵ N/m² and 1.23 kg/m³, respectively (this corresponds to standard sea level conditions). The pressures on the upper and lower surfaces of the wedge are constant with distance \(s\) and equal to each other, namely, \(p_u = p_l = 1.31 \times 10^5\) N/m², as shown in Figure 1.16b. The pressure exerted on the base of the wedge is equal to \(p_\infty\). As seen in Figure 1.16c, the shear stress varies over both the upper and lower surfaces as \(\tau_w = 431s^{-0.2}\). The chord length, \(c\), of the wedge is 2 m. Calculate the drag coefficient for the wedge. **Figures Explanation:** 1. **Figure 1.16a - Flow Field Picture:** - This diagram depicts the side view of the wedge. Key features include: - A 5° wedge body with onset flow at Mach number \(M_\infty = 2\). - Freestream conditions show pressure \(p_\infty = 1.01 \times 10⁵\) N/m² and density \(\rho_\infty = 1.23\) kg/m³. - The wave angle is specified as 34.2°. 2. **Figure 1.16b - Pressure Distribution:** - This diagram illustrates the constant pressure over the wedge surfaces. - The pressure on both the upper and lower surfaces is \(p_u = p_l = 1.31 \times 10⁵\) N/m². - Note the pressures are consistent across the surfaces from the leading to trailing edge of the wedge. 3. **Figure 1.16c - Shear Stress Distribution:** - This graph represents the shear stress distribution over the wedge. - Shear stress \(\tau_w\) is a function of the distance \(s\) along the chord of the wedge, given
Transcribed Image Text:**Example: Supersonic Wedge** **Problem Statement:** Consider the supersonic flow over a 5° half-angle wedge at zero angle of attack, as sketched in Figure 1.16a. The freestream Mach number ahead of the wedge is 2.0, and the freestream pressure and density are 1.01 × 10⁵ N/m² and 1.23 kg/m³, respectively (this corresponds to standard sea level conditions). The pressures on the upper and lower surfaces of the wedge are constant with distance \(s\) and equal to each other, namely, \(p_u = p_l = 1.31 \times 10^5\) N/m², as shown in Figure 1.16b. The pressure exerted on the base of the wedge is equal to \(p_\infty\). As seen in Figure 1.16c, the shear stress varies over both the upper and lower surfaces as \(\tau_w = 431s^{-0.2}\). The chord length, \(c\), of the wedge is 2 m. Calculate the drag coefficient for the wedge. **Figures Explanation:** 1. **Figure 1.16a - Flow Field Picture:** - This diagram depicts the side view of the wedge. Key features include: - A 5° wedge body with onset flow at Mach number \(M_\infty = 2\). - Freestream conditions show pressure \(p_\infty = 1.01 \times 10⁵\) N/m² and density \(\rho_\infty = 1.23\) kg/m³. - The wave angle is specified as 34.2°. 2. **Figure 1.16b - Pressure Distribution:** - This diagram illustrates the constant pressure over the wedge surfaces. - The pressure on both the upper and lower surfaces is \(p_u = p_l = 1.31 \times 10⁵\) N/m². - Note the pressures are consistent across the surfaces from the leading to trailing edge of the wedge. 3. **Figure 1.16c - Shear Stress Distribution:** - This graph represents the shear stress distribution over the wedge. - Shear stress \(\tau_w\) is a function of the distance \(s\) along the chord of the wedge, given
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