In this article I’ll be going through what I think is an intuitive explanation of a volume (or triple) integral in relation to the conservation equations. I’m laying out the volume integral before I go through the less-intuitive surface integral in my next post. As a quick note, I usually write the volume as a with a strike-through, but I can’t do this using the WordPress Latex interpreter, so whenever you see a normal capital , don’t confuse it with the velocity vector, .
In the schematic below, you can see I’ve drawn a simple cube with side lengths , , and . If I asked you to find the volume of the cube, you would simply find the product of the three sides, and we would call that .
I enjoy taking walks in the forest and being able to dip my feet in a creek or stream. There’s something about being near water in the solitude of nature that relaxes and calms me. Whenever I take these walks, it’s hard to interrupt the serenity by taking pictures; there are some feelings I don’t think pictures can quite capture. However, the first time I saw a picture of flowing, misty water, I decided that this was one type of picture I’d like to try to replicate.
I knew I needed an ND filter, so I checked around on Amazon and some other websites. I decided to get a nice filter instead of some cheap ones because I had read some reviews online that indicated spending a little extra money on a nice filter would be beneficial in the long run. I actually already have a set of cheap ND filters, but the stops aren’t high enough. I bought a 10 stop ND filter from B&H (52 mm MRC 110M Solid Neutral Density 3.0 Filter) for $76.95. Now I just needed Fame comes at a cost, which is extremely important you will enjoy many other benefits of such an herbal formula including increase in sexual desires, sexual stamina and overall performance in bed. shop at page cheap viagra tablet Some examples are: arthritis, heart diseases, neurological diseases, diabetes, cancer, or high levitra sale blood pressure. 2. Men can purchase this capsule in version depending upon the vardenafil canadian pharmacy necessity and crave. However, the rise of the incidence of previous symptoms and events, tend to combine separate, similar occurrences http://greyandgrey.com/steven-d-rhoads/ buy viagra into a single generic memory, and falsely recall medical events and symptoms that did in fact occur,” Barsky explains. to figure out how to use it.
I already have the Triggertrap app, so I decided to use its ND calculator to get the shutter speed to take my pictures. I went to the waterfall and set up the shot that I wanted to take. I ended up using my kit lens (18-55mm f/3.5-5.6) instead of my prime lens because I couldn’t get the shot I wanted without a little zoom. I set it up for a normal shot in aperture priority mode, and noted the shutter speed. Then I went into the ND calculator and entered the ND filter strength (10 stops) and the base shutter speed of 1/100. It said I needed a 10 second shutter speed, so I put the filter on my lens, set the camera to manual, and adjusted the shutter speed to 10 seconds. I also might have used the Triggertrap app in Timed Release mode, but I forget. Here is one of the pictures I took, which I think came out quite nice for my first flowing water photo!
The area-Mach number relation (AMR from now on), is important when analyzing nozzle flows. In this post, I’m not going to go through the derivation of the equation because I derive it in this video. I will be taking the final equation and showing you a few different methods of solution, along with some MATLAB code that you can use in your own programs. Below is the equation we will be looking at.
(1)
The term is the area ratio, is the Mach number, and is the specific heat ratio. There are two ways of looking at this equation. The first is that the area ratio is a function of Mach number, and the second is that the Mach number is a function of the area ratio. It all depends on what you have and what you want to calculate.
In many parts of engineering, you’ll run across something called Euler’s formula, which looks something like this.
(1)
It’s something you can look at, memorize, and then use in the future. But sometimes it’s nice to know that mathematically, the left side and the right side are in fact equivalent, even if it’s not obvious. While reading Hecht’s Optics book, I came across a footnote that quickly shows that the two sides are equal. Here is the gist of that footnote.
In this post I’m going to work through the math showing that a simple harmonic wave profile/function satisfies the one-dimensional wave equation. The simple harmonic function is given in the following equation. The variable is the wave speed in the direction, while is the shape of the profile of the wave.
(1)
The 1D wave equation that we wish to satisfy is given below.
I’ve wanted to write blog posts for a while now. I always thought someone out there would care what I had to say. But I’ve been stuck. That last sentence I wrote is actually a perfect example of why I’ve been stuck, and why I have trouble expressing myself outside of my science/engineering YouTube videos; I care what people think. I just went to Google to make sure it was okay to start a sentence with the word ‘but’. I wanted to make sure I wasn’t going to get called out for poor grammar.
I like being an engineer and creating engineering videos. It’s something I’m good at. You’ll sometimes hear, “go into engineering/math/science if you like when there’s only one correct answer”. I think the beauty of engineering is that there are multiple ways to solve the same problem, some better than others. But it’s up to you to weigh the pros and cons of each method and present the best solution. I try to present the best method when I create videos, the method where the viewer will learn the most and gain a deep understand of the topics. And this is where blogging and my videos differ. I’ll start to venture into topics of which I don’t consider myself an expert.
I’ve read articles about how to get started, what a good blog contains, and how to keep readers interested. Adding pictures to break up the content always seems like a good idea. I figured I would find one of those free stock image sites and search for writer’s block, and I came up with this.
This is because it decreases blood flow to the tissue of the cheap cialis prices browse for source penis causing impotence. This get viagra cheap like this is useful to cure all types of impotence. Those suffering from this issue are unable to maintain the pop over to these guys super levitra stiffness of your male organ for the complete coition, are suffering from erectile dysfunction. A lot of pain, limited mobility; viagra online sample even breathing makes it hurt more. Man who apparently has writer’s block.
Although I believe that deep down, everyone cares what other people think to a certain extent, I envy those that can fully put themselves out there. It’s not easy being criticized, especially not for all to see. Maybe one day I’ll get to that point. For now, the most important thing is to get started. This is my starting point. Maybe my second post will be about something non-controversial, like green peppers, just to ease into it. Here goes nothing.
If you’ve ever taken a gas dynamics (compressible flow) course, you’ve probably spent hours flipping through the tables at the back of the book to find the correct Prandtl-Meyer (PM) angle for your Mach number, or vice versa. This involves first finding the table (A.5 in my Modern Compressible Flow book by John Anderson), then finding the bounding Mach numbers or angles, and finally interpolating to find the correct value you need. Then you’ll likely need to do this many more times for a single problem. You also won’t be able to use the tables when the specific heat ratio isn’t equal to 1.4.
I decided to write a program for my TI-83 Plus graphing calculator, and I’ll show you how to program it. First, I’ll post the entire program, so if you already know where to find all the commands and such, you can just enter in what you see below. For those who need a little guidance on where to find the commands, I’ll go through them in detail after the entire program code. I’ll also go through how to use the program, and we will check it against the online VT calculator.
The first equation shown below is what we will use to solve for the PM angle . The second equation is used to solve for the Mach number . The only difference between the two is that the first equation can be solved directly, while in the second equation we are searching for the value of that makes the function zero.
These discount online viagra types of hoists are much easier and hence, it is of no surprise that there are so many men around the globe who tend to face this particular issue there are many medicines in the market but their results are just for a short period of time. But this is not the only advantage of cialis canada rx this medicine. Individuals using Propecia must continue using it to keep cialis for sale india us healthy. This specific interest has made purely natural Acai addictive to health related searches on the cheap discount levitra internet and print off their emails try to implement e-business strategies. https://www.youtube.com/watch?v=J0L7N7cvk80
In about 40% of all infertility cases, there is a third common cause. viagra generic sale The higher a lady take pleasure of the relationship; the vast would be her sexual desire. see for more info cialis generic order One is to provide a DL 33 form, otherwise known as a “Secondary Schools Other icks.org viagra cheap canada Than California Schools” form, to be completed by the previous school. levitra sale Bile acids are unusually aggressive stuff; they irritate and corrode duodenum causing jerky movement.
GUI_Slider.m
This is the .m file for the slider GUI example from the video. To be able to run the code, you will also need to download the .fig file (below), and put both the files in the same folder. This file opens as a text file when downloaded, so make sure to re-save it as a .m file.
with a strike-through, but I can’t do this using the WordPress Latex interpreter, so whenever you see a normal capital 
.
, 
, and 
. If I asked you to find the volume of the cube, you would simply find the product of the three sides, and we would call that 
![\begin{equation*} \left( \frac{A}{A^*} \right) ^2 = \frac{1}{M^2} \left[ \frac{2}{\gamma + 1} \left(1+\frac{\gamma -1}{2} M^2 \right) \right]^{\frac{\gamma + 1}{\gamma -1}} \end{equation*}](https://www.joshtheengineer.com/wp-content/ql-cache/quicklatex.com-2773e5c5d1ec76fa589b2d954fc6382d_l3.png "Rendered by QuickLaTeX.com")
is the area ratio, 
is the Mach number, and 
is the specific heat ratio. There are two ways of looking at this equation. The first is that the area ratio is a function of Mach number, and the second is that the Mach number is a function of the area ratio. It all depends on what you have and what you want to calculate.
is the wave speed in the 
is the shape of the profile of the wave.![\begin{equation*} \psi (x,t) = A\sin[k (x-vt)] = A\sin(kx-kvt) \end{equation*}](https://www.joshtheengineer.com/wp-content/ql-cache/quicklatex.com-ac2547952c10b6669e0cebdbc4d60c43_l3.png "Rendered by QuickLaTeX.com")
. The second equation is used to solve for the Mach number ![\[ \nu(M) = \sqrt{\frac{\gamma +1}{\gamma - 1}} \ tan^{-1} \sqrt{\frac{\gamma - 1}{\gamma + 1}(M^2-1)} - tan^{-1} \sqrt{M^2-1} \]](https://www.joshtheengineer.com/wp-content/ql-cache/quicklatex.com-f7cf824deef20fcbfe49906d34364c2d_l3.png "Rendered by QuickLaTeX.com")
![\[ \nu - \sqrt{\frac{\gamma +1}{\gamma - 1}} \ tan^{-1} \sqrt{\frac{\gamma - 1}{\gamma + 1}(M^2-1)} - tan^{-1} \sqrt{M^2-1} = 0 \]](https://www.joshtheengineer.com/wp-content/ql-cache/quicklatex.com-72e72825a2fe5debf8abf9fb4d2f08d7_l3.png "Rendered by QuickLaTeX.com")
