Adding elements

data/bibtex/references.bib

@@ -5562,4 +5562,17 @@ @Book{Warnatz2006
   subtitle  = {Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation},
 }
 
+@Book{White2016,
+  author    = {White, Frank M.},
+  publisher = {McGraw-Hill},
+  title     = {Fluid mechanics},
+  year      = {2016},
+  address   = {New York, NY},
+  edition   = {Eighth},
+  isbn      = {9780073398273},
+  note      = {Includes index and references},
+  pagetotal = {848},
+  ppn_gvk   = {805546197},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}

docs/src/Notebooks/Pluto/darcy-weisbach.jl

@@ -14,6 +14,10 @@ begin
 	using WallyToolbox
 	using ModelingToolkit
 	using NonlinearSolve
+	using PlutoUI: TableOfContents
+	using Symbolics
+
+	TableOfContents()
 end
 
 # ╔═╡ 3f9fdb0e-caab-40df-99f8-cf0e5ec8deff
@@ -247,6 +251,143 @@ end
 # ╔═╡ 8fcaed37-d179-449c-8d43-8d0ad9a6c35e
 mdot_external / mdot_tot, mdot_cool / mdot_tot, mdot_tangential / mdot_tot
 
+# ╔═╡ 6a6ad275-90d9-47d0-8b5e-a3d20efa9b0a
+md"""
+## Experimental
+"""
+
+# ╔═╡ db5fe5d7-e033-43ef-92d3-1dcbf3d64c17
+begin
+	tuplefy(d) = NamedTuple{Tuple(keys(d))}(values(d))
+
+	########
+
+	struct UnsolvableAlgebraicModel <: Exception
+		msg::String
+
+		function UnsolvableAlgebraicModel(vars, pars)
+			return new(
+				"Unable to solve algebraic model containing [$(join(vars, ", "))] " *
+				"by providing only [$(join(pars, ", "))]! Please, revise the " *
+				"setup of the system!"
+			)
+		end
+	end
+
+	function Base.showerror(io::IO, err::UnsolvableAlgebraicModel)
+	   print(io, "UnsolvableAlgebraicModel: ")
+	   print(io, err.msg)
+	end
+
+	########
+
+	struct AlgebraicModel
+		vars::NamedTuple
+		eqns::Vector{Equation}
+		pars::Dict{Symbol, Float64}
+
+		function AlgebraicModel(vars, eqns, pars)
+			vars = Dict(map(v->(Symbol(v), v), vars))
+			return new(tuplefy(vars), eqns, pars)
+		end
+	end
+
+	function replacement_solve(obj::AlgebraicModel)
+		subs = map(v->(v, get(obj.pars, Symbol(v), v)), values(obj.vars))
+		eqns = substitute(obj.eqns, Dict(subs))
+		return eqns
+	end
+
+	function structural_solve(obj::AlgebraicModel)
+		eqns = replacement_solve(obj)
+
+		has_pars = length(obj.pars) > 0
+
+		if has_pars && length(obj.vars) - length(obj.pars) != length(eqns)
+			throw(UnsolvableAlgebraicModel(obj.vars, obj.pars))
+		end
+
+		@mtkbuild ns = NonlinearSystem(eqns, [values(obj.vars)...], [])
+		prob = NonlinearProblem(ns, [], [])
+		sol = solve(prob)
+
+		solved_for = map(e->e.lhs, observed(ns))
+
+		pars = tuplefy(obj.pars)
+		vars = NamedTuple(map(n->(Symbol(n), sol[n]), solved_for))
+		return merge(pars, vars)
+	end
+
+	########
+
+	function perfect_gas_constants(; pars...)
+		vars = @variables begin
+			k,  [bounds = (1, Inf)]
+			R,  [bounds = (0, Inf)]
+			cp, [bounds = (0, Inf)]
+			cv, [bounds = (0, Inf)]
+		end
+
+		eqns = [
+			0 ~ cp - k * cv,
+			0 ~ cv - R / (k - 1)
+		]
+
+		return AlgebraicModel(vars, eqns, pars)
+	end
+
+	function perfect_gas(; pars...)
+		model = perfect_gas_constants(;)
+
+		vars = @variables begin
+			p,  [bounds = (0, Inf)]
+			ρ,  [bounds = (0, Inf)]
+			T,  [bounds = (0, Inf)]
+			h,  [bounds = (0, Inf)]
+			s,  [bounds = (0, Inf)]
+		end
+
+		R = model.vars.R
+		cp = model.vars.cp
+
+		vars = [vars..., values(model.vars)...]
+		eqns = [
+			0 ~ p - ρ * R * T,
+			0 ~ h - cp * T,
+			0 ~ s - cp * log(T) + R * log(p),
+			model.eqns...
+		]
+
+		return AlgebraicModel(vars, eqns, pars)	
+	end
+end
+
+# ╔═╡ be031284-d872-4e1c-b43d-53038b21f8e4
+let
+	model = perfect_gas_constants(; R=208, k=1.67)
+	solution = structural_solve(model)
+end
+
+# ╔═╡ 80dd3540-f5fb-4c2f-b6d5-b39ad599b8d5
+let
+	R = 208.0
+	k = 1.67
+
+	model1 = perfect_gas(; R, k, p=1.70e+06, ρ=18.0)
+	model2 = perfect_gas(; R, k, p=2.48e+05, T=400.0)
+
+	sol1 = structural_solve(model1)
+	sol2 = structural_solve(model2)
+
+	Δh = sol2.h - sol1.h
+	Δs = sol2.s - sol1.s
+
+	Δh, Δs
+end
+
+# ╔═╡ 3e85af5c-7160-4b60-9369-dfa9dad34f7e
+
+
 # ╔═╡ Cell order:
 # ╟─3f9fdb0e-caab-40df-99f8-cf0e5ec8deff
 # ╟─dcfd03a0-8b23-11ef-202f-0557552ecc92
@@ -275,3 +416,8 @@ mdot_external / mdot_tot, mdot_cool / mdot_tot, mdot_tangential / mdot_tot
 # ╟─067d1351-7739-4d14-a5c7-203a4e86bb59
 # ╟─3357de42-e48c-4e4d-a7df-58d916a1c9b5
 # ╟─8fcaed37-d179-449c-8d43-8d0ad9a6c35e
+# ╟─6a6ad275-90d9-47d0-8b5e-a3d20efa9b0a
+# ╠═db5fe5d7-e033-43ef-92d3-1dcbf3d64c17
+# ╠═be031284-d872-4e1c-b43d-53038b21f8e4
+# ╠═80dd3540-f5fb-4c2f-b6d5-b39ad599b8d5
+# ╠═3e85af5c-7160-4b60-9369-dfa9dad34f7e

docs/src/References/@White2016.md

@@ -0,0 +1,6 @@
+---
+title: "Fluid mechanics"
+authors: Frank M. White
+year: 2016
+---
+

docs/src/Science/01-Continuum-Mechanics.md

@@ -341,6 +341,48 @@ In this expression the *big-D* notation represents a material or convective deri
 
 ### Compressible flow
 
+This topic is discussed as treated in ([[@White2016]]) and based on [Pr. Dr. John Biddle's](https://www.cpp.edu/meonline/fluid-mechanics.shtml) course. The most important parameter in this case is the #Mach number, defined as the ratio of fluid velocity with respect to the velocity of sound in the medium. Increasing Mach number above certain levels introduces the phenomena of *choking* (duct flow rate sharply limited by sonic condition) and *shock waves* (nearly discontinuous property changes in supersonic flow).
+
+- Compressible flows $Ma > 0.3$ (non-negligible density changes introduced)
+- Continuity, momentum, energy, and state equations are coupled
+- Simplification regimes: reversible adiabatic and isentropic flows
+
+- External (aerodynamic) flow regions:
+	- $Ma<0.3$: incompressible flow
+	- $Ma\in[0.3; 0.8]$: subsonic flow
+	- $Ma\in[0.8; 1.2]$: transonic flow
+	- $Ma\in[1.2; 3.0]$: supersonic flow
+	- $Ma>3.0$: hypersonic flows
+
+- Internal (duct) flow regions can be more simply be categorized as subsonic ($Ma<1$) and supersonic ($Ma\ge{}1$) flows.
+
+- Specific heat ratio: generally between 1-1.7 for gases, slowly decreases with temperature; for air a value of 1.4 is generally employed in calculations.
+
+- Ideal gas is generally used for elementary computations; ideal gas constant is used in what follows $\Lambda=8314{}J\cdotp{}kmol^{-1}\cdotp{}K^{-1}$.
+
+$$
+\begin{align*}
+p &= \rho{}RT\\[12pt]
+R &= c_p - c_v = \dfrac{\Lambda}{M}\\[12pt]
+k &= \dfrac{c_p}{c_v}
+\end{align*}
+$$
+
+- Using the above expressions and first and second laws of thermodynamics one shows the following; this expression can be used to compute the entropy change across a shock wave.
+
+$$
+s_2 - s_1 =
+c_p\ln\dfrac{T_2}{T_1}-R\ln\dfrac{p_2}{p_1}=
+c_v\ln\dfrac{T_2}{T_1}-R\ln\dfrac{\rho_2}{\rho_1}
+$$
+
+- For isentropic flows these expressions simplify to the following power-laws:
+
+$$
+\dfrac{p_2}{p_1}=
+\left(\dfrac{T_2}{T_1}\right)^\dfrac{k}{k-1}=
+\left(\dfrac{\rho_2}{\rho_1}\right)^k
+$$
 
 
 ---

docs/src/Science/02-Continuum-Mechanics.md

@@ -176,7 +176,15 @@ which is a manifestation of fluctuation-dissipation theorem. This can be extende
 ![@video]()
 
 ---
-## Biddle course
+## Biddle course on fluid mechanics
+
+### 026 Introduction to compressible flow
+
+![@video](https://www.youtube.com/embed/ewoUwCVa3QY?si=9XWMLZl9VCPmPuFy)
+
+
+---
+## Biddle course on heat transfer
 
 ### 015 Introduction to radiation