Which choice is the differential , incompressible, two-dimensional continuity equation in Cartesian coordinates? ∫ C S ρ V → ⋅ n → d A = 0 1 r ∂ ( r u r ) ∂ r + 1 r ∂ ( u g ) ∂ θ = 0 ∇ → ⋅ ( ρ V → ) = 0 ∇ → ⋅ ∇ → = 0 ∂ u ∂ x + ∂ u ∂ y = 0
Which choice is the differential , incompressible, two-dimensional continuity equation in Cartesian coordinates? ∫ C S ρ V → ⋅ n → d A = 0 1 r ∂ ( r u r ) ∂ r + 1 r ∂ ( u g ) ∂ θ = 0 ∇ → ⋅ ( ρ V → ) = 0 ∇ → ⋅ ∇ → = 0 ∂ u ∂ x + ∂ u ∂ y = 0
Solution Summary: The author describes the differential, incompressible, two-dimensional continuity equation in Cartesian coordinates.
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Using MATLAB , find the magnitude and phase plot of the compensators
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4-81 The corner shown in Figure P4-81 is initially uniform at 300°C and then suddenly
exposed to a convection environment at 50°C with h 60 W/m². °C. Assume the
=
2
solid has the properties of fireclay brick. Examine nodes 1, 2, 3, 4, and 5 and deter-
mine the maximum time increment which may be used for a transient numerical
calculation.
Figure P4-81
1
2
3
4
1 cm
5
6
1 cm
2 cm
h, T
+
2 cm
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A union feedback control system has the following open loop transfer function
where k>0 is a variable proportional gain
i. for K = 1 , derive the exact magnitude and phase expressions of G(jw).
ii) for K = 1 , identify the gaincross-over frequency (Wgc) [where IG(jo))| 1] and phase cross-overfrequency [where <G(jw) = - 180]. You can use MATLAB command "margin" to obtain there quantities.
iii) Calculate gain margin (in dB) and phase margin (in degrees) ·State whether the closed-loop is stable for K = 1 and briefly justify your answer based on the margin . (Gain marginPhase margin)
iv. what happens to the gain margin and Phase margin when you increase the value of K?you
You can use for loop in MATLAB to check that.Helpful matlab commands : if, bode, margin, rlocus
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