The differential equation for conservation of mass by fluid flow is ( ∇ ⋅ {v} + {∂ rho}/{∂ t} = 0 ). Write this equation in rectangular coordinates, cylindrical coordinates, and spherical coordinates.
a) Rectangular: ( {∂}/{∂ x}({v}ₓ) + {∂}/{∂ y}({v}y) + {∂}/{∂ z}({v}z) + {∂ rho}/{∂ t} = 0 )
b) Cylindrical: ( {1}/{r}{∂}/{∂ r}(r{v}ᵣ) + {1}/{r}{∂}/{∂ θ}({v}θ) + {∂}/{∂ z}({v}z) + {∂ rho}/{∂ t} = 0 )
c) Spherical: ( {1}/{r²}{∂}/{∂ r}(r²{v}ᵣ) + {1}/{rsinθ}{∂}/{∂ θ}(sinθ{v}θ) + {1}/{rsinθ}{∂}/{∂ ϕ}({v}ϕ) + {∂ rho}/{∂ t} = 0 )