fix typos

uni/mmme/1048_thermodynamics_and_fluid_mechanics/fluid_dynamics.md

@@ -22,9 +22,9 @@ These are ideas you need to know about to know what's going on, I guess?
 
 ## Control Volumes
 
-A control volume is a volume with an imaginary boundry to make it easier to analyze the flow of a
+A control volume is a volume with an imaginary boundary to make it easier to analyse the flow of a
 fluid.
-The boundry is drawn where the properties and conditions of the fluid is known, or where an
+The boundary is drawn where the properties and conditions of the fluid is known, or where an
 approximation can be made.
 Properties which may be know include:
 
@@ -33,7 +33,7 @@ Properties which may be know include:
 - Temperature
 - Viscosity
 
-The region in the control volume is analyed in terms of enery and mass flows entering and leaving
+The region in the control volume is analysed in terms of energy and mass flows entering and leaving
 the control volumes.
 You don't have to understand what's going on inside the control volume.
 
@@ -50,7 +50,7 @@ momentum or the air passing through the engine.
 ![](./images/vimscrot-2021-11-03T21:51:51,497459693+00:00.png)
 
 The control volume is drawn far enough in front of the engine that the air velocity entering can
-be assumed to be at atmospheric pressurce and its velocity negligible.
+be assumed to be at atmospheric pressure and its velocity negligible.
 
 At the exit of the engine the boundary is drawn close where the velocity is known and the air
 pressure atmospheric.
@@ -97,7 +97,7 @@ with respect to time, like the opposite of steady flow.
 ## One Dimensional Flow
 
 In one dimensional (1D) flow it is assumed that all properties are uniform over any plane
-perpedenciular to the direction of flow (e.g. all points along the cross section of a pipe have
+perpendicular to the direction of flow (e.g. all points along the cross section of a pipe have
 identical properties).
 
 This means properties can only flow in one direction---usually the direction of flow.
@@ -132,7 +132,7 @@ Same reasoning with if they are not parallel.
 ### Pathlines
 
 A pathline shows the route taken by a single particle during a given time interval.
-It is equivalent to a high exposure photograph which traces the moevement of the particle marked.
+It is equivalent to a high exposure photograph which traces the movement of the particle marked.
 You could track pathlines with a drop of injected dye or inserting a buoyant solid particle which
 has the same density as the solid.
 
@@ -222,15 +222,15 @@ Between fully laminar and fully turbulent flows is a transition region.
 
 ### Development of the Reynolds Number
 
-In laminar flow the most influentialfactor is the magnitude of the viscous forces:
+In laminar flow the most influential factor is the magnitude of the viscous forces:
 
 $$viscous\, forces \propto \mu\frac v l l^2 = \mu vl$$
 
-where $v$ is a characteristic velocit and $l$ is a characteristic length.
+where $v$ is a characteristic velocity and $l$ is a characteristic length.
 
 In turbulent flow viscous effects are not significant but inertia effects (mixing, momentum
 exchange, acceleration of fluid mass) are.
-Interial forces can be represented by $F = ma$
+Inertial forces can be represented by $F = ma$
 
 \begin{align*}
 m &\propto \rho l^3 \\
@@ -240,7 +240,7 @@ a &= \frac{dv}{dt} \\
 &\therefore \text{Interial forces} \propto \rho l^2\frac{v^2} l = \rho l^2v^2
 \end{align*}
 
-The ratio of internalforces to viscous forces is called the Reynolds number and is abbreviated to
+The ratio of internal forces to viscous forces is called the Reynolds number and is abbreviated to
 Re:
 
 $$\Rey = \frac{\text{interial forces}}{\text{viscous forces}} = \frac {\rho l^2v^2}{\mu vl} = \frac {\rho vl} \mu$$
@@ -248,12 +248,12 @@ $$\Rey = \frac{\text{interial forces}}{\text{viscous forces}} = \frac {\rho l^2v
 where $\rho$ and $\mu$ are fluid properties and $v$ and $l$ are characteristic velocity and length.
 
 - During laminar flow, $\Rey$ is small as viscous forces dominate.
-- During turbulent flow, $\Rey$ is large as intertial forces dominate.
+- During turbulent flow, $\Rey$ is large as inertial forces dominate.
 
 \textRey is a non dimensional group.
 It has no units because the units cancel out.
 
-Non dimensional groups are very important in fluid mechancics and need to be considered when scaling
+Non dimensional groups are very important in fluid mechanics and need to be considered when scaling
 experiments.
 
 If \textRey is the same in two different pipes, the flow will be the same regardless of actual
@@ -285,7 +285,7 @@ $$\frac 1 \rho \frac{\delta p}{\delta s} + g\frac{\delta z}{\delta s} + v\frac{\
 
 ## Assumptions / Conditions
 
-The Euler euqation applies where the following can be assumed:
+The Euler equation applies where the following can be assumed:
 
 - Steady flow
 - The fluid is inviscid
@@ -350,7 +350,7 @@ $$\frac p {\rho g} + z + \frac{v^2}{2g} = H_T$$
 
 where $H_T$ is constant and:
 
-- $\frac{p}{\rho g}$ --- static/pressure haed
+- $\frac{p}{\rho g}$ --- static/pressure head
 - $z$ --- elevation head
 - $\frac{v_2}{2g}$ --- dynamic/velocity head
 - $H_T$ --- total head
@@ -399,9 +399,9 @@ SFEE is a more general equation that can be applied to **any fluid** and also is
 **heat energy** into account.
 This is useful in applications such as a fan heater, jet engines, ICEs, and steam turbines.
 
-The equation deals with 3 types of energy tranfer:
+The equation deals with 3 types of energy transfer:
 
-1. Thermal energy transfer (e.g. heat tranfer from central heating to a room)
+1. Thermal energy transfer (e.g. heat transfer from central heating to a room)
 2. Work energy transfer (e.g. shaft from car engine that turns wheels)
 3. Energy transfer in fluid flows (e.g. heat energy in a flow, potential energy in a flow, kinetic
    energy in a flow)
@@ -450,7 +450,7 @@ $$\delta E = \delta E_2 - \delta E_1 = \delta m(e_2 - e_1)$$
 
 #### The Work Term
 
-The work term, $\delta W$, is mae up of shaft work **and the work necessary to deform the system**
+The work term, $\delta W$, is made up of shaft work **and the work necessary to deform the system**
 (by adding $\delta m_1$ at the inlet and removing $\delta m_2$ at the outlet):
 
 $$\delta W = \delta W_s + \text{net flow work}$$
@@ -583,7 +583,8 @@ However be aware that in North America the equation is:
 $$H_f = f \frac{L}{D} \frac{v^2}{2g}$$
 
 Their $f$ (the Darcy Friction Factor) is four times our $f$ (Fanning Friction Factor).
-In mainland Europe, they use $\lambda = 4f_{Fanning}$, which is probably the least confusing version to use.
+In mainland Europe, they use $\lambda = 4f_{Fanning}$, which is probably the least confusing version
+to use.
 
 ### Finding $f$