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a085632759
...
f6ce1dedd6
@ -2,11 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: Bash
|
||||
tags:
|
||||
- linux
|
||||
- shell
|
||||
- programming
|
||||
uuid: a436d67a-1f07-45fb-9241-5dbaa69b4667
|
||||
tags: [ linux, shell, programming ]
|
||||
---
|
||||
|
||||
# `set` builtin[^gnuset]
|
||||
|
@ -2,11 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: Setting Up Nginx and Let's Encrypt in Docker
|
||||
tags:
|
||||
- linux
|
||||
- docker
|
||||
- programming
|
||||
uuid: 2abad576-9921-463b-928d-2381f91488e0
|
||||
tags: [ linux, docker, programming ]
|
||||
---
|
||||
|
||||
# Setting Up Nginx and Let's Encrypt in Docker
|
||||
|
@ -2,11 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: Git
|
||||
tags:
|
||||
- linux
|
||||
- programming
|
||||
- git
|
||||
uuid: 8eb93ba5-72e8-4c25-b1f5-02e25408a14d
|
||||
tags: [ linux, programming, git ]
|
||||
---
|
||||
|
||||
|
||||
|
@ -2,11 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: GNOME is a Whole Mess
|
||||
tags:
|
||||
- gnome
|
||||
- linux
|
||||
- troubleshooting
|
||||
uuid: 635199f2-f2c6-4f94-840f-8f729bde0c13
|
||||
tags: [ gnome, linux, troubleshooting ]
|
||||
---
|
||||
|
||||
Gnome is, like, a whole mess. These are the weird issues I had to solve.
|
||||
|
@ -2,10 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: Go (golang)
|
||||
tags:
|
||||
- golang
|
||||
- programming
|
||||
uuid: 70d24c2e-25f6-4a46-9756-659d13b5149f
|
||||
tags: [ golang, programming ]
|
||||
---
|
||||
|
||||
# Getting Up to Speed With Go
|
||||
|
@ -2,10 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: libvirt
|
||||
tags:
|
||||
- linux
|
||||
- virtualisation
|
||||
uuid: 62c2f458-f701-4075-8e12-d9b9a59efd1f
|
||||
tags: [ linux, virtualisation ]
|
||||
---
|
||||
|
||||
# issues
|
||||
|
@ -2,9 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: Linux
|
||||
tags:
|
||||
- linux
|
||||
uuid: 8ef11516-4afd-4f80-abb8-bdce045e8b65
|
||||
tags: [ linux ]
|
||||
---
|
||||
|
||||
# user stuff
|
||||
|
@ -2,9 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: Postgres
|
||||
tags:
|
||||
- programming
|
||||
uuid: 7e44b054-4b6e-4f8c-b9af-9d4c4bf77878
|
||||
tags: [ programming ]
|
||||
---
|
||||
|
||||
\tableofcontents
|
||||
|
@ -2,14 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: Pulseaudio
|
||||
tags:
|
||||
- pulseaudio
|
||||
- linux
|
||||
- audio
|
||||
- mixing
|
||||
- microphone
|
||||
- sink
|
||||
uuid: 4e251354-9afb-49fd-abd9-fedc9b280a25
|
||||
tags: [ pulseaudio, linux, audio, mixing, microphone, sink ]
|
||||
---
|
||||
|
||||
# Collect and Mix Sound Input From Different Sources {#paMixer}
|
||||
|
@ -2,12 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: Python
|
||||
tags:
|
||||
- docker
|
||||
- python
|
||||
- programming
|
||||
- io
|
||||
uuid: cd5c50f9-66f4-4a3b-b89a-04a20ecd642b
|
||||
tags: [ docker, python, programming, io ]
|
||||
---
|
||||
|
||||
# Issues
|
||||
|
@ -2,13 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: Dell XPS 15 (9570)
|
||||
tags:
|
||||
- dell
|
||||
- xps
|
||||
- xps_15
|
||||
- windows
|
||||
- drivers
|
||||
uuid: 489c3145-b3b8-43e0-b51c-c788977e2907
|
||||
tags: [ dell, xps, xps_15, windows, drivers ]
|
||||
---
|
||||
|
||||
# Installing Windows: A media driver your computer needs is missing.
|
||||
|
@ -2,15 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: MMME1026 // Calculus
|
||||
tags:
|
||||
- uni
|
||||
- nottingham
|
||||
- mechanical
|
||||
- engineering
|
||||
- mmme1026
|
||||
- maths
|
||||
- calculus
|
||||
uuid: 126b21f8-e188-48f6-9151-5407f2b2b644
|
||||
tags: [ uni, nottingham, mechanical, engineering, mmme1026, maths, calculus ]
|
||||
---
|
||||
|
||||
# Calculus of One Variable Functions
|
||||
|
@ -2,15 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: MMME1026 // Complex Numbers
|
||||
tags:
|
||||
- uni
|
||||
- nottingham
|
||||
- mechanical
|
||||
- engineering
|
||||
- mmme1026
|
||||
- maths
|
||||
- complex_numbers
|
||||
uuid: b9be8780-1ab7-402f-9c67-8cc74a74f7a9
|
||||
tags: [ uni, nottingham, mechanical, engineering, mmme1026, maths, complex_numbers ]
|
||||
---
|
||||
|
||||
# Complex Numbers
|
||||
|
@ -2,16 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: MMME1026 // Systems of Equations and Matrices
|
||||
tags:
|
||||
- uni
|
||||
- nottingham
|
||||
- mechanical
|
||||
- engineering
|
||||
- mmme1026
|
||||
- maths
|
||||
- systems_of_equations
|
||||
- matrices
|
||||
uuid: 16edb140-9946-4759-93df-50cad510fe31
|
||||
tags: [ uni, nottingham, mechanical, engineering, mmme1026, maths, systems_of_equations, matrices ]
|
||||
---
|
||||
# Systems of Equations (Simultaneous Equations)
|
||||
|
||||
|
@ -2,15 +2,7 @@
|
||||
author: Akbar Rahman
|
||||
date: \today
|
||||
title: MMME1026 // Vectors
|
||||
tags:
|
||||
- uni
|
||||
- nottingham
|
||||
- mechanical
|
||||
- engineering
|
||||
- mmme1026
|
||||
- maths
|
||||
- vectors
|
||||
uuid: ef1669d9-b8c3-4813-8b33-5764a2f57a55
|
||||
tags: [ uni, nottingham, mechanical, engineering, mmme1026, maths, vectors ]
|
||||
---
|
||||
|
||||
Vectors have a *magnitude* (size) and *direction*.
|
||||
@ -256,7 +248,7 @@ $$\frac{x-x_0}{d_1} = \frac{y-y_0}{d_2} = \frac{z-z_0}{d_3}$$
|
||||
A *plane* can be defined by specifying either:
|
||||
|
||||
- three points (as long as they're not in a straight line)
|
||||
- a point on the plane and two directions (useful for a parametric form)
|
||||
- a point on the plne and two directions (useful for a parametric form)
|
||||
- specifying a point on the plane and the normal vector to the plane
|
||||
|
||||
#### Specifying a Point and a Normal Vector
|
||||
@ -271,7 +263,7 @@ $$(\pmb r - \pmb a) \cdot \pmb n = 0$$
|
||||
|
||||
So the *vector equation* of the plane is
|
||||
|
||||
$$\pmb r \cdot \pmb n = \pmb a \cdot \pmb n = \pmb d$$
|
||||
$$\pmb r \cdot \pmb n = \pmb a \cdot n = d$$
|
||||
|
||||
where $\pmb r = (x, y, z)$ and the vectors $\pmb a$ and $\pmb n$ are known.
|
||||
|
||||
@ -299,7 +291,6 @@ and so the equation of the plane is
|
||||
|
||||
$$(\pmb r - \pmb a)\cdot((\pmb c - \pmb a)\times(\pmb c - \pmb b)) = 0$$
|
||||
|
||||
|
||||
#### The Angle Between Two Planes
|
||||
|
||||
... is the same as the angle between their normal vectors
|
||||
|
@ -11,7 +11,6 @@ tags:
|
||||
- statics
|
||||
- dynamics
|
||||
title: MMME1028 // Statics
|
||||
uuid: 2ddad9d0-b085-4602-aca9-c573351558ba
|
||||
---
|
||||
|
||||
# Lecture L1.1, L1.2
|
||||
|
@ -2,14 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: MMME1029 // Manufacturing
|
||||
tags:
|
||||
- uni
|
||||
- nottingham
|
||||
- mechanical
|
||||
- engineering
|
||||
- mmme1029
|
||||
- manufacturing
|
||||
uuid: b5fae4fd-32c3-4fd8-a05a-7440d6c44f9c
|
||||
tags: [ uni, nottingham, mechanical, engineering, mmme1029, manufacturing ]
|
||||
---
|
||||
|
||||
# Cost Modelling
|
||||
|
@ -2,14 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: MMME1029 // Materials
|
||||
tags:
|
||||
- uni
|
||||
- nottingham
|
||||
- mechanical
|
||||
- engineering
|
||||
- mmme1029
|
||||
- materials
|
||||
uuid: 755626f6-53ae-473a-8ff8-185ca9427bfd
|
||||
tags: [ uni, nottingham, mechanical, engineering, mmme1029, materials ]
|
||||
---
|
||||
|
||||
\tableofcontents
|
||||
|
@ -2,15 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: MMME1048 // Fluid Dynamics
|
||||
tags:
|
||||
- uni
|
||||
- nottingham
|
||||
- mechanical
|
||||
- engineering
|
||||
- fluid_mechanics
|
||||
- mmme1048
|
||||
- fluid_dynamics
|
||||
uuid: b88f78f8-a358-460b-9dbb-812e7b1ace92
|
||||
tags: [ uni, nottingham, mechanical, engineering, fluid_mechanics, mmme1048, fluid_dynamics ]
|
||||
---
|
||||
|
||||
\newcommand\Rey{\mbox{\textit{Re}}}
|
||||
@ -392,157 +384,3 @@ Head form:
|
||||
\frac{p_s}{\rho g} + z + \frac{v^2}{2g} &= \text{total head} \\
|
||||
\frac{p_s}{\rho g} + z &= \text{piezometric head}
|
||||
\end{align*}
|
||||
|
||||
# Steady Flow Energy Equation (SFEE)
|
||||
|
||||
SFEE is a more general equation that can be applied to **any fluid** and also is also takes
|
||||
**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:
|
||||
|
||||
1. Thermal energy transfer (e.g. heat tranfer 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)
|
||||
|
||||
## Derivation of Steady Flow Energy Equation
|
||||
|
||||
#### Consider a control volume with steady flows in and out and steady transfers of work and heat.
|
||||
|
||||
The properties don't change with time at any any location and are considered uniform over inlet and
|
||||
outlet areas $A_1$ and $A_2$.
|
||||
|
||||
For steady flow, the mass, $m$, of the fluid **within the control volume** and the total energy, $E$,
|
||||
must be constant.
|
||||
|
||||
$E$ includes **all forms for energy** but we only consider internal, kinetic, and potential energy.
|
||||
|
||||
#### Consider a small time interval $\delta t$.
|
||||
|
||||
During $\delta t$, mass $\delta m_1$ enters the control volume and $\delta m_2$ leaves:
|
||||
|
||||
![](./images/vimscrot-2022-03-01T22:47:31,932087932+00:00.png)
|
||||
|
||||
The specific energy $e_1$ of fluid $\delta m_1$ is the sum of the specific internal energy, specific
|
||||
kinetic energy, and specific potential energy:
|
||||
|
||||
$$e_1 = u_1 + \frac{v_1^2}{2} gz_1$$
|
||||
$$e_2 = u_2 + \frac{v_2^2}{2} gz_2$$
|
||||
|
||||
Since the mass is constant in the control volume, $\delta m_1 = \delta m_2$.
|
||||
|
||||
#### Applying the First Law of Thermodynamics
|
||||
|
||||
The control volume is a system for which $\delta E_1$ is added and $\delta E_2$ is removed::
|
||||
|
||||
$$\delta E = \delta E_2 - \delta E_1$$
|
||||
|
||||
$E$ is constant so applying the
|
||||
[first law of thermodynamics](thermodynamics.html#st-law-of-thermodynamics)
|
||||
we know that:
|
||||
|
||||
$$\delta Q + \delta W = \delta E$$
|
||||
|
||||
We can also say that:
|
||||
|
||||
$$\delta E = \delta E_2 - \delta E_1 = \delta m(e_2 - e_1)$$
|
||||
|
||||
#### The Work Term
|
||||
|
||||
The work term, $\delta W$, is mae up of shaft work **and the work necessary to deform the system**
|
||||
(by adding $\delta m_1$ at the inlet and removing $\delta m_2$ at the outlet):
|
||||
|
||||
$$\delta W = \delta W_s + \text{net flow work}$$
|
||||
|
||||
Work is done **on** the system by the mass entering and **by** the system on the mass leaving.
|
||||
|
||||
For example, at the inlet:
|
||||
|
||||
![](./images/vimscrot-2022-03-01T22:59:14,129582752+00:00.png)
|
||||
|
||||
$$\text{work done on system} = \text{force} \times \text{distance} = p_1A_1\delta x = p_1\delta V_1$$
|
||||
|
||||
Knowing this, we can write:
|
||||
|
||||
$$\delta W = \delta W_s + (p_1\delta V_1 - p_2\delta V_2)$$
|
||||
|
||||
#### Back to the First Law
|
||||
|
||||
Substituting these equations:
|
||||
|
||||
$$\delta E = \delta E_2 - \delta E_1 = \delta m(e_2 - e_1)$$
|
||||
$$\delta W = \delta W_s + (p_1\delta V_1 - p_2\delta V_2)$$
|
||||
|
||||
into:
|
||||
|
||||
$$\delta Q + \delta W = \delta E$$
|
||||
|
||||
gives us:
|
||||
|
||||
$$\delta Q + \left[ \delta W_s + (p_1\delta V_1 - p_2\delta V_2)\right] = \delta m (e_2-e_1)$$
|
||||
|
||||
Dividing everything by $\delta m$ and with a bit of rearranging we get:
|
||||
|
||||
$$q + w_s = e_2-e_1 + \frac{p_2}{\rho_2} - \frac{p_1}{\rho_1}$$
|
||||
|
||||
#### Substiute Back for $e$
|
||||
|
||||
$$e = u + \frac{v^2}{2} + gz$$
|
||||
|
||||
This gives us:
|
||||
|
||||
$$q + w_s + \left[ u_2 + \frac{p_2}{\rho_2} + gz_2 + \frac{v_2^2}{2} \right] - \left[ u_1 + \frac{p_1}{\rho_1} + gz_1 + \frac{v_1^2}{2} \right]$$
|
||||
|
||||
#### Rearrange and Substitute for Enthalpy
|
||||
|
||||
By definition, enthalpy $h = u + pv = u + \frac p \rho$.
|
||||
This gives us the equation:
|
||||
|
||||
$$q + w_s = (h_2 - h_1) + g(z_2-z_1) + \frac{v_2^2-v_1^2}{2}$$
|
||||
|
||||
This equation is in specific energy form.
|
||||
|
||||
Multiplying by mass flow rate will give you the power form.
|
||||
|
||||
## Application of the Steady Flow Energy Equation
|
||||
|
||||
#### Heat Transfer Devices
|
||||
|
||||
Like heat exchangers, boilers, condensers, and furnaces.
|
||||
|
||||
In this case, $\dot W = 0$, $\delta z ~ 0$, and $\delta v^2 ~ 0$ so the equation can be simplified
|
||||
to just
|
||||
|
||||
$$\dot Q = \dot m(h_2-h_1) = \dot m c_p(T_2-T_1)$$
|
||||
|
||||
#### Throttle Valve
|
||||
|
||||
No heat and work transfer.
|
||||
Often you can neglect potential and kinetic energy terms, giving you:
|
||||
|
||||
$$0 = h_2-h_1)$$
|
||||
|
||||
#### Work Transfer Devices
|
||||
|
||||
e.g. Turbines, Pumps, Fans, and Compressors
|
||||
|
||||
For these there is often no heat transfer ($\dot Q = 0$) and we can neglect potential
|
||||
($\delta z ~ 0$) and kinetic ($\delta v^2 ~ 0$) energy terms, giving us the equation
|
||||
|
||||
$$\dot W = \dot m (h_2-h_1) = \dot m c_p(T_2-T_1)$$
|
||||
|
||||
#### Mixing Devices
|
||||
|
||||
e.g. hot and cold water in a shower
|
||||
|
||||
In these processes, work and heat transfers are not important and you can often
|
||||
neglect potential and kinetic energy terms, giving us the same equation as for the throttle valve
|
||||
earlier:
|
||||
|
||||
$$0 = h_2-h_1$$
|
||||
|
||||
which you may want to write more usefully as:
|
||||
|
||||
$$\sum \dot m h_{out} = \sum \dot m h_{in}$$
|
||||
|
||||
|
@ -2,15 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: MMME1048 // Fluid Mechanics Intro and Statics
|
||||
tags:
|
||||
- uni
|
||||
- nottingham
|
||||
- mechanical
|
||||
- engineering
|
||||
- fluid_mechanics
|
||||
- mmme1048
|
||||
- fluid_statics
|
||||
uuid: 43e8eefa-567f-438b-b93d-63ae08e61d8f
|
||||
tags: [ uni, nottingham, mechanical, engineering, fluid_mechanics, mmme1048, fluid_statics ]
|
||||
---
|
||||
|
||||
# Properties of Fluids
|
||||
|
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@ -2,14 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: MMME1048 // Thermodynamics
|
||||
tags:
|
||||
- uni
|
||||
- nottingham
|
||||
- mechanical
|
||||
- engineering
|
||||
- mmme1048
|
||||
- thermodynamics
|
||||
uuid: db8abbd9-1ef4-4a0d-a6a8-54882f142643
|
||||
tags: [ uni, nottingham, mechanical, engineering, mmme1048, thermodynamics ]
|
||||
---
|
||||
|
||||
# What is Thermodynamics?
|
||||
|
@ -2,11 +2,7 @@
|
||||
author: Alvie Rahman
|
||||
date: \today
|
||||
title: Applied Technology
|
||||
tags:
|
||||
- uni
|
||||
- university_of_sussex
|
||||
- applied_technology
|
||||
uuid: 0ec5e507-b024-4594-800a-131cbbe83619
|
||||
tags: [ uni, university_of_sussex, applied_technology ]
|
||||
---
|
||||
|
||||
<details>
|
||||
|
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Reference in New Issue
Block a user