×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

35

0

2

# 144 CribSheet for M E 521 at PSU

Marketplace > Pennsylvania State University > 144 CribSheet for M E 521 at PSU

No professor available

These notes were just uploaded, and will be ready to view shortly.

Either way, we'll remind you when they're ready :)

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

## Popular in Department

This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 35 views.

×

## Reviews for 144 CribSheet for M E 521 at PSU

×

×

### What is Karma?

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15
Equation Sheet for Midterm Exam ME 521 prepared by Professor J M Cimbala Tensor transformation rules for rotation Cy 2 cos 01 tensorA A CW4 lAgm CWC Ay rump Epsilondelta relatio CWC Ckvljkl etc 3 gykglorm xm jn 755 m m Cross product ax 1k eykaxb Gauss Stokes and Leibniz theorems G 0F dV FdA lax i I where 04 angle between the old 139 and new j axes Then for S A maangina C Vz Material derivative DF 0F 0F u Dr 0t 0x Strain rate tensor 1 1 7 w 11 V d r 7 mm s r a E I FxtdV7 I wa c nmm dA Vz A Reynolds transport theorem Conservation of mas 2 t Wt J39FdV J39ng CJSFujdAJ CV CS for any uid Principal strain rates eigenvalues found from 50Iat CV a palV qipujdA CS 0x 1 Conservation of momentum following a uid particle where F is some variable det ey 7 MV 0 where F can be any quantity per unit volume 0 0 0 0139 39 39 dV dA dV dA V For any fluld gym pul ipulu1 J 5ng in J atltpux 0xpuxu1 pgx 0x i p Dr pg 0x Constitutive equation relation between stress and strain with 0 defined as the devialaric stress tensor Ty 7p61 011 For Newtonian fluid TV ipdy Z ey lemmde and the famous N avierStokes equation results EmI EmI 0p 0 BuI 071 0 071 p u 7 pgx u A 01 J 0x 6xI 0x 0x 6x1 6x1 0x au au 0 2 For incam ressible ow 139 7 5 2 8 u 7 p V pV J p 0t 10x1 0x1 pg axjax Incompressible conservation equations of mass and momentum in Cartesian coordinates xyz 0 0 0w 02 02 02 a 0 0 u V V2 2 2 2 Vu v w 0x By 02 0x By 02 0x By 02 Bu Bu Bu Bu 7 2 azu azu u V w 7 0 at 0x ay 02 0 pgx a 2 yz 022 0 aVu V rip 0 u azvazvazv at 0x 02 ay gy 0x2 yz 022 0w 0w 0w 0w 02w02w02w u V w 7 0 at 0x 02 az pgl 1 0x2 yz 022 an 1 1 Bu 0v 1 0v 1 0v Bu a X X g wz 0x 2 xx y 2 0y 0x 2 y W 0y 2 W 0x 0y Incompressible conservation equations of mass and momentum in cylindrical coordinates re z 1 0 1 0 0 1 0 0 1 02 02 a 0 0 0 m u u0 V2 r 2 2 2 aVu i uz r 0r r 09 02 r Br Br r 09 02 Or r 09 02 au39 u au39 lu9 au39 uz au39 flu 7la p g v Via fizu 732 01 Or r 00 02 r p 0r r r 00 0 0 0 amp 39lu9ampuz luru9 0Pg9 W V2 izug 32 01 Or r 00 02 r p r 00 r r 00 3 59 2 lip zwwzuz 01 Or r 02 p 02 0a 1 10 a 1 r 0 M5 1 0M 1 n n 955 055 er 0y5 0r 2n r06 r 2n 20r r Zr 09 2 1 0 1 0a z ltmigti r 0r r 09 BE 0 0M Mechanical energy equation uE puxgx L39yux p 7 Rate ofv1scous d1551pat10n of kmetlc 01 0x x 0x 0a 1 energy per unlt volume E V Dev1ator1c stress tensor 0quot TV pde Kmetlc energy per unlt volume EE fpuJt x J First Law Heat equation 1pe ixuI Jdl l CJSpe ixuI ujdA ngxude CJSz39yudi 7 J qxolAI CS CV CS CS CV D 0 0g De g 0a eiuu u ru 7 7 7 th 2 mg 0xy 0x th 0x1 paxx DT air DT D 0 0T If incompressible pCpEkaxxaxx 2 eyey Ifidealgas pCpEFIaxka Ifidealgas alvery low DT OZT Mach number pC F Dt fixxfixI The Tds equations of Thermodynamics Tds ale de Tds db 7 Udp Where T temperature p pressure e specific internal energy h specific enthalpy s specific entropy and U 1 0 specific volume Bernoulli equations For incompressible steady irrolalional flow can be viscous q2 g2 constant 0 For incompressible steady inviscid flow can be rotational q2 g2 constant along a streamline 0 For steady compressible inviscid irrolalional isenlropic flow 11 q2 g2 constant 11 E e g 0 F a 8 Interaction of Vortices Veloc1ty 1nduced by one vortex on 1ts ne1ghbors M5 2 Where F E c1rculat10n qSu ds In C a a Do 0a 020 Vorticity equation for incompressible Newtonian ow k co V quot Di 0x axjax

×

×

### BOOM! Enjoy Your Free Notes!

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

Jim McGreen Ohio University

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Allison Fischer University of Alabama

#### "I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over \$600 per month. I LOVE StudySoup!"

Jim McGreen Ohio University

Forbes

#### "Their 'Elite Notetakers' are making over \$1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!
×

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com