Documentation: fluid dynamics

symplyphysics/laws/hydro/dynamic_pressure_via_density_and_flow_speed.py

@@ -2,9 +2,8 @@
 Dynamic pressure from speed
 ===========================
 
-*Dynamic pressure*, sometimes called *velocity pressure*, is a physical quantity denoting the
-pressure caused by a flowing fluid. It is numerically equal to the kinetic energy of the
-fluid per unit volume (see :doc:`laws.quantities.quantity_is_volumetric_density_times_volume`).
+**Dynamic pressure**, sometimes called **velocity pressure**, is a physical quantity denoting the
+pressure caused by a flowing fluid.
 
 **Notes:**
 
@@ -16,43 +15,29 @@
 #. `Wikipedia <https://en.wikipedia.org/wiki/Dynamic_pressure>`__.
 """
 
-from sympy import (Eq, solve)
-from symplyphysics import (units, Quantity, Symbol, validate_input, validate_output)
+from sympy import Eq, solve
+from symplyphysics import Quantity, validate_input, validate_output, symbols
 
-dynamic_pressure = Symbol("dynamic_pressure", units.pressure)
+dynamic_pressure = symbols.dynamic_pressure
 """
-Dynamic pressure of the fluid.
-
-Symbol:
-    :code:`q`
+:symbols:`dynamic_pressure` of the fluid. 
 """
 
-density = Symbol("density", units.mass / units.volume)
-r"""
-Density of the fluid.
-
-Symbol:
-    :code:`rho`
-
-Latex:
-    :math:`\rho`
+density = symbols.density
 """
-
-flow_speed = Symbol("flow_speed", units.velocity)
+:symbols:`density` of the fluid.
 """
-Flow speed of the fluid.
 
-Symbol:
-    :code:`u`
+flow_speed = symbols.flow_speed
+"""
+:symbols:`flow_speed` of the fluid.
 """
 
 law = Eq(dynamic_pressure, density * flow_speed**2 / 2)
-r"""
-:code:`q = 1/2 * rho * u^2`
+"""
+:laws:symbol::
 
-Latex:
-    .. math::
-        q = \frac{1}{2} \rho u^2
+:laws:latex::
 """
 
 

symplyphysics/laws/hydro/efficiency_of_the_hydraulic_press_from_force_and_height.py

@@ -1,50 +1,71 @@
+"""
+Efficiency of hydraulic press from force and height
+===================================================
+
+A real hydraulic press is never :math:`100%` efficient due to friction and other energy
+losses. Its efficiency is the ratio of the useful work (given by the product of output
+force and the height of the output side) to the expended work (given by the product of
+input force and the height of the input side).
+
+..
+    TODO: find link
+"""
+
 from sympy import Eq, solve
 from symplyphysics import (
     clone_as_symbol,
     symbols,
-    units,
     Quantity,
-    Symbol,
     validate_input,
     validate_output,
-    dimensionless,
     convert_to_float,
 )
 
-# Description
-## Since the hydraulic press is a mechanism, its operation can be characterized by a coefficient of efficiency.
+output_force = clone_as_symbol(symbols.force, subscript="2")
+"""
+Output :symbols:`force`.
+"""
+
+output_distance = clone_as_symbol(symbols.euclidean_distance, subscript="2")
+"""
+:symbols:`euclidean_distance` covered by the output piston.
+"""
+
+input_force = clone_as_symbol(symbols.force, subscript="1")
+"""
+Input :symbols:`force`.
+"""
 
-## Law: n = (F2 * h2) / (F1 * h1)
-## Where:
-## F2 is the force spent on useful work (work on lifting the load)
-## h2 is the movement of load
-## F1 is expended force
-## h1 is expended height
-## n is coefficient of efficiency
+input_distance = clone_as_symbol(symbols.euclidean_distance, subscript="1")
+"""
+:symbols:`euclidean_distance` covered by the input piston.
+"""
 
-# TODO find link
+efficiency = symbols.mechanical_efficiency
+"""
+:symbols:`mechanical_efficiency` of the hydraulic press.
+"""
 
-useful_force = clone_as_symbol(symbols.force, display_symbol="F_1", display_latex="F_1")
-useful_height = Symbol("useful_height", units.length)
-expended_force = clone_as_symbol(symbols.force, display_symbol="F_2", display_latex="F_2")
-expended_height = Symbol("expended_height", units.length)
-efficiency = Symbol("efficiency", dimensionless)
+law = Eq(efficiency, (output_force * output_distance) / (input_force * input_distance))
+"""
+:laws:symbol::
 
-law = Eq(efficiency, (useful_force * useful_height) / (expended_force * expended_height))
+:laws:latex::
+"""
 
 
-@validate_input(useful_force_=useful_force,
-    useful_height_=useful_height,
-    expended_force_=expended_force,
-    expended_height_=expended_height)
+@validate_input(useful_force_=output_force,
+    useful_height_=output_distance,
+    expended_force_=input_force,
+    expended_height_=input_distance)
 @validate_output(efficiency)
 def calculate_efficiency(useful_force_: Quantity, useful_height_: Quantity,
     expended_force_: Quantity, expended_height_: Quantity) -> float:
     result_expr = solve(law, efficiency, dict=True)[0][efficiency]
     result_efficiency = result_expr.subs({
-        useful_force: useful_force_,
-        useful_height: useful_height_,
-        expended_force: expended_force_,
-        expended_height: expended_height_
+        output_force: useful_force_,
+        output_distance: useful_height_,
+        input_force: expended_force_,
+        input_distance: expended_height_
     })
     return convert_to_float(result_efficiency)

symplyphysics/laws/hydro/efflux_speed_via_height.py

@@ -2,8 +2,12 @@
 Efflux speed via height
 =======================
 
-The speed of a fluid flowing out from a small orifice can be expressed as a function
-of the height of the fluid column. It is also known as the *Torricelli's law*.
+The speed of a fluid flowing out from a small orifice can be expressed as a function of
+the height of the fluid column. It is also known as the **Torricelli's law**.
+
+**Notation:**
+
+#. :quantity_notation:`acceleration_due_to_gravity`.
 
 **Conditions:**
 
@@ -16,32 +20,24 @@
 #. `Wikipedia <https://en.wikipedia.org/wiki/Torricelli%27s_law#>`__.
 """
 
-from sympy import (Eq, solve, sqrt)
-from symplyphysics import (units, Quantity, Symbol, validate_input, validate_output)
+from sympy import Eq, solve, sqrt
+from symplyphysics import Quantity, validate_input, validate_output, symbols, quantities
 
-efflux_speed = Symbol("efflux_speed", units.velocity)
+efflux_speed = symbols.flow_speed
 """
-Speed of the fluid flowing out of the pipe.
-
-Symbol:
-    :code:`v`
+:symbols:`flow_speed` of the fluid flowing out of the pipe.
 """
 
-height = Symbol("height", units.length)
+height = symbols.height
 """
-Height of the fluid column above the orifice.
-
-Symbol:
-    :code:`h`
+:symbols:`height` of the fluid column above the orifice.
 """
 
-law = Eq(efflux_speed, sqrt(2 * units.acceleration_due_to_gravity * height))
-r"""
-:code:`v = sqrt(2 * g * h)`
+law = Eq(efflux_speed, sqrt(2 * quantities.acceleration_due_to_gravity * height))
+"""
+:laws:symbol::
 
-Latex:
-    .. math::
-        v = \sqrt{2 g h}
+:laws:latex::
 """
 
 # TODO Derive from Bernoulli's equation and constancy of volume flux

symplyphysics/laws/hydro/efflux_speed_via_hydrostatic_pressure_and_density.py

@@ -15,52 +15,32 @@
     TODO find link
 """
 
-from sympy import (Eq, solve, sqrt)
-from symplyphysics import (
-    units,
-    Quantity,
-    Symbol,
-    validate_input,
-    validate_output,
-)
+from sympy import Eq, solve, sqrt
+from symplyphysics import Quantity, validate_input, validate_output, symbols
 from symplyphysics.core.expr_comparisons import expr_equals
 from symplyphysics.laws.hydro import hydrostatic_pressure_via_density_and_height as pressure_law
 from symplyphysics.laws.hydro import efflux_speed_via_height as velocity_law
 
-efflux_speed = Symbol("efflux_speed", units.velocity)
+efflux_speed = symbols.flow_speed
 """
-Speed of the fluid flowing out of the pipe.
-
-Symbol:
-    :code:`v`
+:symbols:`flow_speed` of the fluid flowing out of the pipe.
 """
 
-hydrostatic_pressure = Symbol("hydrostatic_pressure", units.pressure)
+hydrostatic_pressure = symbols.hydrostatic_pressure
 """
-Hydrostatic pressure of the fluid.
-
-Symbol:
-    :code:`p`
+:symbols:`hydrostatic_pressure` of the fluid.
 """
 
-density = Symbol("density", units.mass / units.volume)
-r"""
-Density of the fluid.
-
-Symbol:
-    :code:`rho`
-
-Latex:
-    :math:`\rho`
+density = symbols.density
+"""
+:symbols:`density` of the fluid.
 """
 
 law = Eq(efflux_speed, sqrt(2 * hydrostatic_pressure / density))
-r"""
-:code:`v = sqrt(2 * p / rho)`
+"""
+:laws:symbol::
 
-Latex:
-    .. math::
-        v = \sqrt{\frac{2 p}{\rho}}
+:laws:latex::
 """
 
 # This law might be derived via "hydrostatic_pressure_from_density_and_depth" law

symplyphysics/laws/hydro/excessive_pressure_under_curved_surface_of_bubble.py

@@ -1,55 +1,73 @@
-from sympy import (Eq, solve)
-from symplyphysics import (units, Quantity, Symbol, validate_input, validate_output)
-from symplyphysics.core.expr_comparisons import expr_equals
+"""
+Excess pressure under curved surface of bubble
+==============================================
 
-from symplyphysics.laws.thermodynamics import laplace_pressure_of_spherical_shapes as laplace_law
+Under the curved surface of the liquid, in addition to the internal pressure, additional
+pressure is created due to the curvature of the surface. For a bubble, this pressure is
+created by two surfaces: the outer and the inner.
+
+**Links:**
+
+#. `Physics LibreTexts, formula 20.2.4 <https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Tatum)/20%3A_Miscellaneous/20.02%3A_Surface_Tension/20.2.01%3A_Excess_Pressure_Inside_Drops_and_Bubbles>`__.
 
-# Description
-## Under the curved surface of the liquid, in addition to the internal pressure,
-## additional pressure is created due to the curvature of the surface.
-## For a bubble, this pressure is created by two surfaces: the outer and the inner.
+..
+    TODO: fix file name
+"""
+
+from sympy import Eq, solve
+from symplyphysics import Quantity, validate_input, validate_output, symbols, clone_as_symbol
+from symplyphysics.core.expr_comparisons import expr_equals
+from symplyphysics.laws.thermodynamics import laplace_pressure_of_spherical_shapes as laplace_law
 
-## Law is: p = 4 * sigma / R, where
-## p - excessive pressure under the curved surface of bubble,
-## sigma - surface tension of the liquid,
-## R - radius of bubble.
+pressure_difference = clone_as_symbol(symbols.pressure, display_symbol="Delta(p)", display_latex="\\Delta p")
+"""
+:symbols:`pressure` difference between the surfaces of the bubble.
+"""
 
-# Links: Physics LibreTexts, formula 20.2.4 <https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Classical_Mechanics_(Tatum)/20%3A_Miscellaneous/20.02%3A_Surface_Tension/20.2.01%3A_Excess_Pressure_Inside_Drops_and_Bubbles>
+surface_tension = symbols.surface_tension
+"""
+:symbols:`surface_tension` of the bubble.
+"""
 
-excessive_pressure = Symbol("excessive_pressure", units.pressure)
+radius = symbols.radius
+"""
+:symbols:`radius` of the bubble.
+"""
 
-surface_tension_of_the_liquid = Symbol("surface_tension_of_the_liquid", units.force / units.length)
-radius_of_bubble = Symbol("radius_of_bubble", units.length)
+law = Eq(pressure_difference, 4 * surface_tension / radius)
+"""
+:laws:symbol::
 
-law = Eq(excessive_pressure, 4 * surface_tension_of_the_liquid / radius_of_bubble)
+:laws:latex::
+"""
 
 # This law might be derived via Laplace law.
 
 # TODO prefix all variables used in proof with underscore
 
-laplace_law_applied = laplace_law.law.subs({
-    laplace_law.surface_tension: surface_tension_of_the_liquid,
-    laplace_law.radius_of_curvature: radius_of_bubble
+_laplace_law_applied = laplace_law.law.subs({
+    laplace_law.surface_tension: surface_tension,
+    laplace_law.radius_of_curvature: radius
 })
 
 # This is an excess pressure in a spherical drop.
-pressure_derived = solve(laplace_law_applied, laplace_law.laplace_pressure,
+_pressure_derived = solve(_laplace_law_applied, laplace_law.laplace_pressure,
     dict=True)[0][laplace_law.laplace_pressure]
 
 # Check if derived pressure is same as declared.
 # The bubble has two surfaces – an outer and an inner one, each of which creates additional pressure.
 # Therefore, an additional multiplier of "2" appears.
-assert expr_equals(2 * pressure_derived, law.rhs)
+assert expr_equals(2 * _pressure_derived, law.rhs)
 
 
-@validate_input(surface_tension_of_the_liquid_=surface_tension_of_the_liquid,
-    radius_of_bubble_=radius_of_bubble)
-@validate_output(excessive_pressure)
+@validate_input(surface_tension_of_the_liquid_=surface_tension,
+    radius_of_bubble_=radius)
+@validate_output(pressure_difference)
 def calculate_excessive_pressure(surface_tension_of_the_liquid_: Quantity,
     radius_of_bubble_: Quantity) -> Quantity:
-    solved = solve(law, excessive_pressure, dict=True)[0][excessive_pressure]
+    solved = solve(law, pressure_difference, dict=True)[0][pressure_difference]
     result_expr = solved.subs({
-        surface_tension_of_the_liquid: surface_tension_of_the_liquid_,
-        radius_of_bubble: radius_of_bubble_
+        surface_tension: surface_tension_of_the_liquid_,
+        radius: radius_of_bubble_
     })
     return Quantity(result_expr)