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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Isentropic expansion waves ： ウィキペディア英語版 Isentropic expansion waves are created when a supersonic flow is redirected along a curved surface. These waves are studied to obtain a relation between deflection angle and Mach number. Each wave in this case is a Mach wave, so it is at an angle \alpha = sin^(\frac) , where M is the Mach number immediately before the wave. Expansion waves are divergent because as the flow expands the value of Mach number increases, thereby decreasing the Mach angle.In an isentropic wave, the speed changes from v to (v + dv), with deflection d \theta. We have oriented the coordinate system orthogonal to the wave. We write the basic (continuity, momentum and 1st, 2nd law of thermodynamics) equations for this infinitesimal control volume.Assumptions'':''''' Isentropic expansion waves are created when a supersonic flow is redirected along a curved surface. These waves are studied to obtain a relation between deflection angle and Mach number. Each wave in this case is a Mach wave, so it is at an angle $\backslash alpha\; =\; sin^(\backslash frac)$ , where M is the Mach number immediately before the wave. Expansion waves are divergent because as the flow expands the value of Mach number increases, thereby decreasing the Mach angle. In an isentropic wave, the speed changes from $v$ to $(v\; +\; dv)$, with deflection $d\; \backslash theta$. We have oriented the coordinate system orthogonal to the wave. We write the basic (continuity, momentum and 1st, 2nd law of thermodynamics) equations for this infinitesimal control volume. Assumptions'':'' # Steady flow. # Negligible body forces. # Adiabatic flow. # No work terms. # Negligible gravitational effect. ==Relation between θ,M and v== The continuity equation is, $\backslash frac\backslash int\backslash limits\_\backslash rho\; dV\; +\backslash int\backslash limits\_\backslash rho\; \backslash bar\; v.d\backslash bar\; A=0$ .......(1.1) First term is zero by ''assumption(1)''. Now, $+\; =0$ or $\backslash rho\; v\; \backslash sin\backslash alpha\; =(\backslash rho+\; d\backslash rho)(v+dv)\backslash sin(\backslash alpha-d\backslash theta)$...... (1.2) Now we consider the momentum equation for normal and tangential to shock. For $y$- component, $F\_+F\_=\backslash frac\backslash int\backslash limits\_v\_y\backslash rho\; dV\; +\backslash int\backslash limits\_v\_y\backslash rho\; \backslash bar\; v.d\backslash bar\; A$......(1.3) Second term of L.H.S and first term of R.H.S are zero due to ''assumption (2) and (1) respectively''. Then, $0=v\backslash cos\backslash alpha(-\backslash rho\; v\; \backslash sin\backslash alpha\; A)\; +\; (v+dv)\backslash cos(\backslash alpha\; -\; d\backslash theta)$ Or using continuity, $v\backslash cos\backslash alpha=(v+dv)\backslash cos(\backslash alpha-d\backslash theta)$ Expanding and simplifying (the facts that, to the first order, in the limit as $d\backslash theta\backslash rightarrow\; 0$, $\backslash cos\backslash rightarrow\; 1$ and $\backslash sin\; \backslash rightarrow\; d\backslash theta$ ), we obtain $d\backslash theta=\backslash frac$ But, $\backslash sin\backslash alpha=\backslash frac$, so, $\backslash tan\backslash alpha=\backslash fracdv\}$ ......(1.4) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「'''Isentropic expansion''' waves are created when a supersonic flow is redirected along a curved surface. These waves are studied to obtain a relation between deflection angle and Mach number. Each wave in this case is a Mach wave, so it is at an angle \alpha = sin^(\frac) , where M is the Mach number immediately before the wave. Expansion waves are divergent because as the flow expands the value of Mach number increases, thereby decreasing the Mach angle.In an isentropic wave, the speed changes from v to (v + dv), with deflection d \theta. We have oriented the coordinate system orthogonal to the wave. We write the basic (continuity, momentum and 1st, 2nd law of thermodynamics) equations for this infinitesimal control volume.Assumptions''''':'''''」の詳細全文を読む ':'' Isentropic expansion waves are created when a supersonic flow is redirected along a curved surface. These waves are studied to obtain a relation between deflection angle and Mach number. Each wave in this case is a Mach wave, so it is at an angle $\backslash alpha\; =\; sin^(\backslash frac)$ , where M is the Mach number immediately before the wave. Expansion waves are divergent because as the flow expands the value of Mach number increases, thereby decreasing the Mach angle. In an isentropic wave, the speed changes from $v$ to $(v\; +\; dv)$, with deflection $d\; \backslash theta$. We have oriented the coordinate system orthogonal to the wave. We write the basic (continuity, momentum and 1st, 2nd law of thermodynamics) equations for this infinitesimal control volume. Assumptions'':'' # Steady flow. # Negligible body forces. # Adiabatic flow. # No work terms. # Negligible gravitational effect. ==Relation between θ,M and v== The continuity equation is, $\backslash frac\backslash int\backslash limits\_\backslash rho\; dV\; +\backslash int\backslash limits\_\backslash rho\; \backslash bar\; v.d\backslash bar\; A=0$ .......(1.1) First term is zero by ''assumption(1)''. Now, $+\; =0$ or $\backslash rho\; v\; \backslash sin\backslash alpha\; =(\backslash rho+\; d\backslash rho)(v+dv)\backslash sin(\backslash alpha-d\backslash theta)$...... (1.2) Now we consider the momentum equation for normal and tangential to shock. For $y$- component, $F\_+F\_=\backslash frac\backslash int\backslash limits\_v\_y\backslash rho\; dV\; +\backslash int\backslash limits\_v\_y\backslash rho\; \backslash bar\; v.d\backslash bar\; A$......(1.3) Second term of L.H.S and first term of R.H.S are zero due to ''assumption (2) and (1) respectively''. Then, $0=v\backslash cos\backslash alpha(-\backslash rho\; v\; \backslash sin\backslash alpha\; A)\; +\; (v+dv)\backslash cos(\backslash alpha\; -\; d\backslash theta)$ Or using continuity, $v\backslash cos\backslash alpha=(v+dv)\backslash cos(\backslash alpha-d\backslash theta)$ Expanding and simplifying (the facts that, to the first order, in the limit as $d\backslash theta\backslash rightarrow\; 0$, $\backslash cos\backslash rightarrow\; 1$ and $\backslash sin\; \backslash rightarrow\; d\backslash theta$ ), we obtain $d\backslash theta=\backslash frac$ But, $\backslash sin\backslash alpha=\backslash frac$, so, $\backslash tan\backslash alpha=\backslash fracdv\}$ ......(1.4) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「'''Isentropic expansion''' waves are created when a supersonic flow is redirected along a curved surface. These waves are studied to obtain a relation between deflection angle and Mach number. Each wave in this case is a Mach wave, so it is at an angle \alpha = sin^(\frac) , where M is the Mach number immediately before the wave. Expansion waves are divergent because as the flow expands the value of Mach number increases, thereby decreasing the Mach angle.In an isentropic wave, the speed changes from v to (v + dv), with deflection d \theta. We have oriented the coordinate system orthogonal to the wave. We write the basic (continuity, momentum and 1st, 2nd law of thermodynamics) equations for this infinitesimal control volume.Assumptions''''':'''''」の詳細全文を読む ' Isentropic expansion waves are created when a supersonic flow is redirected along a curved surface. These waves are studied to obtain a relation between deflection angle and Mach number. Each wave in this case is a Mach wave, so it is at an angle $\backslash alpha\; =\; sin^(\backslash frac)$ , where M is the Mach number immediately before the wave. Expansion waves are divergent because as the flow expands the value of Mach number increases, thereby decreasing the Mach angle. In an isentropic wave, the speed changes from $v$ to $(v\; +\; dv)$, with deflection $d\; \backslash theta$. We have oriented the coordinate system orthogonal to the wave. We write the basic (continuity, momentum and 1st, 2nd law of thermodynamics) equations for this infinitesimal control volume. Assumptions'':'' # Steady flow. # Negligible body forces. # Adiabatic flow. # No work terms. # Negligible gravitational effect. ==Relation between θ,M and v== The continuity equation is, $\backslash frac\backslash int\backslash limits\_\backslash rho\; dV\; +\backslash int\backslash limits\_\backslash rho\; \backslash bar\; v.d\backslash bar\; A=0$ .......(1.1) First term is zero by ''assumption(1)''. Now, $+\; =0$ or $\backslash rho\; v\; \backslash sin\backslash alpha\; =(\backslash rho+\; d\backslash rho)(v+dv)\backslash sin(\backslash alpha-d\backslash theta)$...... (1.2) Now we consider the momentum equation for normal and tangential to shock. For $y$- component, $F\_+F\_=\backslash frac\backslash int\backslash limits\_v\_y\backslash rho\; dV\; +\backslash int\backslash limits\_v\_y\backslash rho\; \backslash bar\; v.d\backslash bar\; A$......(1.3) Second term of L.H.S and first term of R.H.S are zero due to ''assumption (2) and (1) respectively''. Then, $0=v\backslash cos\backslash alpha(-\backslash rho\; v\; \backslash sin\backslash alpha\; A)\; +\; (v+dv)\backslash cos(\backslash alpha\; -\; d\backslash theta)$ Or using continuity, $v\backslash cos\backslash alpha=(v+dv)\backslash cos(\backslash alpha-d\backslash theta)$ Expanding and simplifying (the facts that, to the first order, in the limit as $d\backslash theta\backslash rightarrow\; 0$, $\backslash cos\backslash rightarrow\; 1$ and $\backslash sin\; \backslash rightarrow\; d\backslash theta$ ), we obtain $d\backslash theta=\backslash frac$ But, $\backslash sin\backslash alpha=\backslash frac$, so, $\backslash tan\backslash alpha=\backslash fracdv\}$ ......(1.4) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「'''Isentropic expansion''' waves are created when a supersonic flow is redirected along a curved surface. These waves are studied to obtain a relation between deflection angle and Mach number. Each wave in this case is a Mach wave, so it is at an angle \alpha = sin^(\frac) , where M is the Mach number immediately before the wave. Expansion waves are divergent because as the flow expands the value of Mach number increases, thereby decreasing the Mach angle.In an isentropic wave, the speed changes from v to (v + dv), with deflection d \theta. We have oriented the coordinate system orthogonal to the wave. We write the basic (continuity, momentum and 1st, 2nd law of thermodynamics) equations for this infinitesimal control volume.Assumptions''''':'''''」の詳細全文を読む ':''">ウィキペディア（Wikipedia）』 ■ウィキペディアで「'''Isentropic expansion''' waves are created when a supersonic flow is redirected along a curved surface. These waves are studied to obtain a relation between deflection angle and Mach number. Each wave in this case is a Mach wave, so it is at an angle \alpha = sin^(\frac) , where M is the Mach number immediately before the wave. Expansion waves are divergent because as the flow expands the value of Mach number increases, thereby decreasing the Mach angle.In an isentropic wave, the speed changes from v to (v + dv), with deflection d \theta. We have oriented the coordinate system orthogonal to the wave. We write the basic (continuity, momentum and 1st, 2nd law of thermodynamics) equations for this infinitesimal control volume.Assumptions''''':'''''」の詳細全文を読む '">ウィキペディア（Wikipedia）』 ■ウィキペディアで「'''Isentropic expansion''' waves are created when a supersonic flow is redirected along a curved surface. These waves are studied to obtain a relation between deflection angle and Mach number. Each wave in this case is a Mach wave, so it is at an angle \alpha = sin^(\frac) , where M is the Mach number immediately before the wave. Expansion waves are divergent because as the flow expands the value of Mach number increases, thereby decreasing the Mach angle.In an isentropic wave, the speed changes from v to (v + dv), with deflection d \theta. We have oriented the coordinate system orthogonal to the wave. We write the basic (continuity, momentum and 1st, 2nd law of thermodynamics) equations for this infinitesimal control volume.Assumptions''''':'''''」の詳細全文を読む ':''">ウィキペディアで「'''Isentropic expansion''' waves are created when a supersonic flow is redirected along a curved surface. These waves are studied to obtain a relation between deflection angle and Mach number. Each wave in this case is a Mach wave, so it is at an angle \alpha = sin^(\frac) , where M is the Mach number immediately before the wave. Expansion waves are divergent because as the flow expands the value of Mach number increases, thereby decreasing the Mach angle.In an isentropic wave, the speed changes from v to (v + dv), with deflection d \theta. We have oriented the coordinate system orthogonal to the wave. We write the basic (continuity, momentum and 1st, 2nd law of thermodynamics) equations for this infinitesimal control volume.Assumptions''''':'''''」の詳細全文を読む '">ウィキペディアで「Isentropic expansion waves are created when a supersonic flow is redirected along a curved surface. These waves are studied to obtain a relation between deflection angle and Mach number. Each wave in this case is a Mach wave, so it is at an angle \alpha = sin^(\frac) , where M is the Mach number immediately before the wave. Expansion waves are divergent because as the flow expands the value of Mach number increases, thereby decreasing the Mach angle.In an isentropic wave, the speed changes from v to (v + dv), with deflection d \theta. We have oriented the coordinate system orthogonal to the wave. We write the basic (continuity, momentum and 1st, 2nd law of thermodynamics) equations for this infinitesimal control volume.Assumptions'':'''''」の詳細全文を読む ':''」の詳細全文を読む '」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.