fix typos

uni/mmme/1048_thermodynamics_and_fluid_mechanics/fluid_mechanics.md

@@ -17,22 +17,20 @@ uuid: 43e8eefa-567f-438b-b93d-63ae08e61d8f
 
 ## What is a Fluid?
 
-- A fluid may be liquid, vapor, or gas
+- A fluid may be liquid, vapour, or gas
 - No permanent shape
 - Consists of atoms in random motion and continual collision
 - Easy to deform
 - Liquids have fixed volume, gasses fill up container
-- **A fluid is a substance for wich a shear stress tends to produce unlimited, continuous
+- **A fluid is a substance for which a shear stress tends to produce unlimited, continuous
   deformation**
 
 ## Shear Forces
 
 - For a solid, application of shear stress causes a deformation which, if not too great (elastic),
-  is not permanent and solid regains original positon
-- For a fluid, continuious deformation takes place as the molecules slide over each other until the
+  is not permanent and solid regains original position
+- For a fluid, continuous deformation takes place as the molecules slide over each other until the
   force is removed
-- **A fluid is a substance for wich a shear stress tends to produce unlimited, continuous
-  deformation**
 
 ## Density
 
@@ -51,7 +49,7 @@ uuid: 43e8eefa-567f-438b-b93d-63ae08e61d8f
 
 - Matter is not continuous on molecular scale
 - For fluids in constant motion, we take a time average
-- For most practical purposes, matter is considered to be homogenous and time averaged
+- For most practical purposes, matter is considered to be homogeneous and time averaged
 
 ## Pressure
 
@@ -77,7 +75,7 @@ uuid: 43e8eefa-567f-438b-b93d-63ae08e61d8f
 
 - A fluid at rest has constant pressure horizontally
 - That's why liquid surfaces are flat
-- But fluids at rest do have a vertical gradient, where lower parts have higher presure 
+- But fluids at rest do have a vertical gradient, where lower parts have higher pressure 
 
 ### How Does Pressure Vary with Depth?
 
@@ -116,11 +114,11 @@ The -ve sign indicates that as $z$, height, increases, $p$, pressure, decreases.
 ### Absolute and Gauge Pressure
 
 - Absolute Pressure is measured relative to zero (a vacuum)
-- Guage pressure = absolute pressure - atmospheric pressure
+- Gauge pressure = absolute pressure - atmospheric pressure
 
   - Often used in industry
 
-- If abs. pressure = 3 bar and atmospheric pressure is 1 bar, then gauge pressure = 2 bar
+- If absolute pressure = 3 bar and atmospheric pressure is 1 bar, then gauge pressure = 2 bar
 - Atmospheric pressure changes with altitude
 
 ## Compressibility
@@ -132,7 +130,7 @@ The -ve sign indicates that as $z$, height, increases, $p$, pressure, decreases.
 ## Surface Tension
 
 - In a liquid, molecules are held together by molecular attraction
-- At a boundry between two fluids this creates "surface tension"
+- At a boundary between two fluids this creates "surface tension"
 - Surface tension usually has the symbol $$\gamma$$
 
 ## Ideal Gas
@@ -155,7 +153,7 @@ The -ve sign indicates that as $z$, height, increases, $p$, pressure, decreases.
   - Pressure always in Pa
   - Temperature always in K
 
-## Units and Dimentional Analysis
+## Units and Dimensional Analysis
 
 - It is usually better to use SI units
 - If in doubt, DA can be useful to check that your answer makes sense
@@ -289,7 +287,7 @@ p_1 - p_2 &= \rho_wg(z_C-z_B-z_C+z_A) + \rho_mg\Delta z \\
    the upper surface (figure 1.4).  The tank and riser are filled with 
    water such that the water level in the riser pipe is 3.5 m above the 
 
-   Calulate:
+   Calculate:
 
    i. The gauge pressure at the base of the tank. 
 
@@ -299,7 +297,7 @@ p_1 - p_2 &= \rho_wg(z_C-z_B-z_C+z_A) + \rho_mg\Delta z \\
 
        > $$\rho gh = 1000\times9.81\times3.5 = 34 \text{ kPa}$$
 
-   iii. The force exercted on the base of the tank due to gauge water pressure.
+   iii. The force exerted on the base of the tank due to gauge water pressure.
 
         > $$F = p\times A = 49\times10^3\times6\times3 = 8.8\times10^5 \text{ N}$$
 
@@ -345,7 +343,7 @@ p_1 - p_2 &= \rho_wg(z_C-z_B-z_C+z_A) + \rho_mg\Delta z \\
 
 ## Submerged Surfaces
 
-### Prepatory Maths
+### Preparatory Maths
 
 #### Integration as Summation
 
@@ -370,7 +368,7 @@ Take the following lamina:
 1. Split the lamina into elements parallel to the chosen axis
 2. Each element has area $\delta A = w\delta y$
 3. The moment of area ($\delta M$) of the element is $\delta Ay$
-4. The sum of moments of all the elements is equal to the moment $M$ obtained by assuing all the
+4. The sum of moments of all the elements is equal to the moment $M$ obtained by assuming all the
    area is located at the centroid or:
 
    $$Ay_c = \int_{area} \! y\,\mathrm{d}A$$
@@ -426,7 +424,7 @@ Determine the location of the centroid of a rectangular lamina.
 
 </details>
 
-### Horizontal Submereged Surfaces
+### Horizontal Submerged Surfaces
 
 ![](./images/vimscrot-2021-10-20T10:33:16,783724117+01:00.png)
 
@@ -492,12 +490,12 @@ Where $\rho$ is the density of the fluid, and $V$ is the volume of displaced flu
 ### Immersed Bodies
 
 As pressure increases with depth, the fluid exerts a resultant upward force on a body.
-There is no horizontal component of the buoyancy force because the vertiscal projection of the body
+There is no horizontal component of the buoyancy force because the vertical projection of the body
 is the same in both directions.
 
 ### Rise, Sink, or Float?
 
-- $F_B = W$ \rightarrow equilirbrium (floating)
+- $F_B = W$ \rightarrow equilibrium (floating)
 - $F_B > W$ \rightarrow body rises
 - $F_B < W$ \rightarrow body sinks