Algebraic equations such as Bernoulli's relation, Bq. (1) of Example 1.3, are dimensionally consistent, but what about differential equations? Consider, for example, the boundary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904: ρ u ∂ u ∂ x + ρ v ∂ u ∂ y = − ∂ p ∂ x + ρ g x + ∂ τ ∂ y where t is the boundary-layer shear stress and g x is the component of gravity in the x direction. Is this equation dimen-sionally consistent? Can you draw a general conclusion?
Algebraic equations such as Bernoulli's relation, Bq. (1) of Example 1.3, are dimensionally consistent, but what about differential equations? Consider, for example, the boundary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904: ρ u ∂ u ∂ x + ρ v ∂ u ∂ y = − ∂ p ∂ x + ρ g x + ∂ τ ∂ y where t is the boundary-layer shear stress and g x is the component of gravity in the x direction. Is this equation dimen-sionally consistent? Can you draw a general conclusion?
Algebraic equations such as Bernoulli's relation, Bq. (1) of Example 1.3, are dimensionally consistent, but what about differential equations? Consider, for example, the boundary-layer x-momentum equation, first derived by Ludwig Prandtl in 1904:
ρ
u
∂
u
∂
x
+
ρ
v
∂
u
∂
y
=
−
∂
p
∂
x
+
ρ
g
x
+
∂
τ
∂
y
where t is the boundary-layer shear stress and gx is the component of gravity in the x direction. Is this equation dimen-sionally consistent? Can you draw a general conclusion?
The 120 kg wheel has a radius of gyration of 0.7 m. A force P with a magnitude of 50 N is applied at the edge of the wheel as seen in the diagram. The coefficient of static friction is 0.3, and the coefficient of kinetic friction is 0.25. Find the acceleration and angular acceleration of the wheel.
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Using MATLAB , find the magnitude and phase plot of the compensators
NO COPIED SOLUTIONS
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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