Do calculations for the lab report

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lab1/lab1.pdf

Lab Name Abbreviated Report AE341 Lab Reports

Your Name Here

September 6, 2016

Date Performed: Month Day, Year Group : “Letter Here “ Instructor: Professor Torres

Nomenclature

ṁ Mass Flow Q Volumetric Flow Rate A Area, units u Velocity, units ρ Density

1 Introduction

Objective of lab from lab manual.

2 Theory

The volumetric flow rate is defined as

Q = uA. (1)

Multiplying by the fluid density the mass flow rate, ṁ, is defined as

ṁ = ρuA. (2)

3 Test Procedure & Equipment

The water table at SDSU was used with a vertical jet apparatus seen in Figure 1.

Figure 1: Vertical Jet Momentum Apparatus.

Two plates were used a flat plate with beta 90◦ and a hemispherical plate with beta 180◦

seen in Figure 2.

Figure 2: Caption goes here. Replace caption.

4 Results and Discussion

The results can be seen in table 1 . The difference in slope between theory and experimental for the flat plate was “value here” %. The difference in slope between theory and experimental for the hemispherical plate was “value here” %. An experimental bias of “value here” was found for the flat plate. An experimental bias of “value here” was found for the hemispherical plate. The correlation value for the flat plate was “value here”. The correlation value for the hemispherical plate was “value here”.

4.1 Source of Error

Discuss error types, and causes during your experiment.

Table 1: Comparison Table Theory Exp % Error Theoretical Experimental Correlation Slope Slope Slope Bias Bias Value

Flat Plate 1 X X X X X Hemispherical 2 X X X X X

Plate

4.2 Questions

1. Suppose the jet of water is inclined 10◦ from vertical. For the 180◦ deflector

a) What effect would this have on the measured force( give a value and percentage increase or decrease in force)? answer

b) How would this affect the slope? answer

c) How would this affect the bias? answer

2. If the jockey weight is not correctly zeroed by .1 cm, what would you expect the bias to be? Discuss

3. Explain at least one additional reason for observed slope or bias error? answer

4. If your data was not within experimental error, give a probable cause. answer

Graphs

Figure 3: Graph Name Here.

Least Square Fit Calculations

Correlation, Bias & Error Calculations

Test Data

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!12646
}2
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{3
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g1	113:10988933	8774387
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g1	113:30193281	8774387
(1	114:30193281	8774387:4593852	665187	285084
g1	113:30586497	8774387
k1	113:32201579	8774387:1615082
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k1	114:34393917	8774387:1615081
g1	114:34787133	8774387
g1	114:34774026	8774387
r1	114:34800240	8774387:26214	950271	285084
g1	114:34787133	8774387
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g1	114:34787133	8774387
)
(1	115:5471305	9724658:29315828	665187	285084
g1	114:5471305	9724658
(1	114:5471305	9724658:5517628	665187	285084
r1	114:5471305	9724658:0	950271	285084
g1	114:5458198	9724658
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g1	114:5471305	9724658
g1	114:5864521	9724658
g1	114:5864521	9724658
g1	114:5864522	9724658
x1	114:10595717	9724658
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g1	114:10975826	9724658
r1	114:11002040	9724658:26214	950271	285084
g1	114:10988933	9724658
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g1	114:10988933	9724658
(1	114:10988933	9724658:3203502	665187	285084
g1	114:11382149	9724658
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g1	114:14192435	9724658
g1	114:14179328	9724658
r1	114:14205542	9724658:26214	950271	285084
g1	114:14192435	9724658
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g1	114:14192435	9724658
(1	114:14192435	9724658:2604582	665187	285084
g1	114:14585651	9724658
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g1	114:16797017	9724658
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g1	114:16797017	9724658
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g1	114:17190233	9724658
k1	114:18254454	9724658:1064221
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g1	114:20276041	9724658
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g1	114:20289148	9724658
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g1	114:20289148	9724658
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g1	114:20682364	9724658
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g1	114:24883000	9724658
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g1	114:24883000	9724658
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g1	114:25276216	9724658
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g1	114:30193281	9724658
g1	114:30180174	9724658
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g1	114:30193281	9724658
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g1	114:30193281	9724658
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g1	114:30586497	9724658
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g1	115:34787133	9724658
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g1	115:34787133	9724658
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g1	115:10988933	10674929
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g1	115:10988933	10674929
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g1	115:16797017	10674929
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!20125
}3
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{4
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Input:30:S:\GASCOMPR\RTorres\other\teaching\lab1\lab1.aux
!66
Postamble:
Count:1331
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Post scriptum:

lab1/lab1.tex

\documentclass[12pt,letterpaper]{article} \usepackage{fullpage} \usepackage{parskip} \usepackage{setspace} \usepackage{verbatim} \usepackage{mathtools} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{float} %\usepackage[small,center,bf]{caption} % ----------------- % Document title % ----------------- \title{Lab Name Abbreviated Report % Replace with Lab Name \\AE341 Lab Reports} \author{ Your Name Here } % Replace with your name \begin{document} \maketitle \begin{center} \begin{tabular}{l r} Date Performed: & Month Day, Year \\ % Date the experiment was performed Group : & ``Letter Here `` \\ Instructor: & Professor Torres % Instructor/supervisor \end{tabular} \end{center} \section*{Nomenclature} % nomenclature is only necessary when including equations \begin{tabbing} XXX \= \kill% this line sets tab stop $\dot{m}$ \> Mass Flow \\ $Q$ \> Volumetric Flow Rate \\ $A$ \> Area, units \\ $u$ \> Velocity, units \\ $\rho$ \> Density \end{tabbing} \section{Introduction} % Introduction is always necessary Objective of lab from lab manual. \section{Theory} % short summation for abbreviated lab The volumetric flow rate is defined as \begin{equation} \label{e:Q} Q = u A. \end{equation} Multiplying by the fluid density the mass flow rate, $\dot{m} $, is defined as \begin{equation} \label{e:function3} \dot{m} = \rho u A. \end{equation} \section{Test Procedure \& Equipment} %short summation for abbreviated labs The water table at SDSU was used with a vertical jet apparatus seen in Figure~\ref{f:equip}. \begin{figure}[h] \begin{center} \includegraphics[width=1.5in]{equipment} \caption{Vertical Jet Momentum Apparatus.} \label{f:equip} \end{center} \end{figure} Two plates were used a flat plate with beta 90$^\circ$ and a hemispherical plate with beta 180$^\circ$ seen in Figure~\ref{f:plate}. \begin{figure}[h] \begin{center} \includegraphics[width=1.5in]{beta} \caption{Caption goes here. Replace caption.} \label{f:plate} \end{center} \end{figure} \section{Results and Discussion} % always required in all reports The results can be seen in table~\ref{t:example} . The difference in slope between theory and experimental for the flat plate was ``value here'' \%. The difference in slope between theory and experimental for the hemispherical plate was ``value here'' \%. An experimental bias of ``value here'' was found for the flat plate. An experimental bias of ``value here'' was found for the hemispherical plate. The correlation value for the flat plate was ``value here''. The correlation value for the hemispherical plate was ``value here''. \subsection{Source of Error} % always required in all reports, not neccesary to be a separate subsection. Can be included as part of the results and discussion section. Discuss error types, and causes during your experiment. % Example of how to setup tables. Always include results in 4 forms. Written, Table, Graph, Raw Data. \begin{table} [h] % Replace X with actual values in table \begin{center} \caption{Comparison Table} \label{t:example} \begin{tabular}{|r| c | c | c | c | c | c | c l} \hline & Theory & Exp & \% Error & Theoretical & Experimental & Correlation\\ & Slope & Slope & Slope & Bias & Bias & Value\\ \hline Flat Plate & 1 & X & X & X &X & X \\ Hemispherical & 2 & X & X & X & X &X \\ Plate & &&&&& \\ \hline \end{tabular} \end{center} \end{table} \subsection{Questions} 1. Suppose the jet of water is inclined 10$^\circ$ from vertical. For the 180$^\circ$ deflector a) What effect would this have on the measured force( give a value and percentage increase or decrease in force)? answer b) How would this affect the slope? answer c) How would this affect the bias? answer\\ 2. If the jockey weight is not correctly zeroed by .1 cm, what would you expect the bias to be? Discuss 3. Explain at least one additional reason for observed slope or bias error? answer 4. If your data was not within experimental error, give a probable cause. answer % additional stuff in this order for all reports. Graphs, Calculations, Test Data \clearpage \begin{center} \section*{Graphs} \end{center} \begin{figure}[h] \begin{center} \includegraphics[width=6.75in]{graph} \caption{Graph Name Here.} \label{f:graph} \end{center} \end{figure} \clearpage \begin{center} \section*{Least Square Fit Calculations} \end{center} \clearpage \begin{center} \section*{Correlation, Bias \& Error Calculations} \end{center} \clearpage \begin{center} \section*{Test Data} \end{center} \end{document} % - Release $Name: $ -