### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Fluid Mechanics EGR 365

GVSU

GPA 3.68

### View Full Document

## 58

## 0

## Popular in Course

## Popular in Engineering and Tech

This 15 page Class Notes was uploaded by Tyree Funk on Saturday September 26, 2015. The Class Notes belongs to EGR 365 at Grand Valley State University taught by Shirley Fleischmann in Fall. Since its upload, it has received 58 views. For similar materials see /class/214376/egr-365-grand-valley-state-university in Engineering and Tech at Grand Valley State University.

## Reviews for Fluid Mechanics

### What is Karma?

#### Karma is the currency of StudySoup.

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

Date Created: 09/26/15

Impact of a Fluid Jet by Dan Schwarz School of Engineering Grand Valley State University EGR 365 7 Fluid Mechanics Section 01 Instructor Dr S Fleischmann June 19 2007 Outline 1 Purpose Statement a The impact force of a jet of air striking a perpendicular surface was calculated using control volume analysis b An experimental system was used to verify the calculation 11 Background a The experimental system is shown in Figure 1 Air is blown at a constant mass ow rate into the control volume The air jet strikes the beam and then leaves the control volume in two different directions The mass ow rate of the air leaving the control volume is equal to the mass ow rate of air entering the control volume H A128x10395m3 Figure 1 The experimental system is a cantilever beam that deforms from the impact force of the airjet b The impact reaction force was determined using the conservation of momentum principal Equation 1 was used to calculate the reaction force as a function of the mass ow rate See Appendix A for details Appendix B and C show how the air density and velocity was calculated 2 2 m Ry pv A p p14 A c Experimental Method 39 The air nozzle was removed from the system and its inner diameter was measured Four different masses were placed on the top of the cantilever beam and the de ections were measured These de ections where used to create a calibration curve that relates beam de ection to the resultant force Ry iii The air nozzle was replaced and the air valve was opened until the mass ow rate reached 2 gramssecond iv The de ection of the beam was measured Steps iii and iv were repeated with mass ow rates ranging from 3 to 9 grams second lt vi The calibration curve was used to determine the reaction forces based on the beam de ection III Results Discussion a The reaction forces measured in the experimental procedure are compared with the forces predicted using Equation 1 Mass 0 Flow Rate A1rVmeloc1ty De ection Predicted Experimental o s m Force N Force N Discrepancy b The discrepancy begins to grow as the air velocity approaches the speed of sound At the room temperature of 26 C the speed of sound was approximately 346 ms Table 1 shows that the discrepancy increases dramatically at 338497 ms and continues to grow as the velocity increases c The divergence of experimental and predicted reaction forces is shown in Figure Reaction Force N Reaction Force vs Mass FlowRate 6 5 4 9 Predicted Reaction 3 l Experimental 2 Reaction 0000 0002 0004 0006 0008 0010 Mass Flow Rate kgs Figure 2 Predicted and experimental reaction forces are compared graphically IV Conclusions a The experimental results show that control volume analysis can successfully predict the impact reaction force produced by a uid jet However this prediction becomes inaccurate when the uid velocity approaches the speed of sound V Appendices a Appendix A 7 Question 1 i Find the reaction force using control volume analysis 1 Begin with the general conservation of momentum equation d A A A A ZFy 7EJLvadVvavndl4 2 Unnecessary terms drop out ZFy 0Ry 7va7 dA 3 Simplify Ry J39 adv an vaA b Appendix B 7 Question 2 i Find the density of the air at room temperature 1 Begin with the ideal gas law P pRT 2 Solve for density 7 P p 7 RT 3 Substitute values into the equation and solve numerically 990mbaer 00 Pambar kg 11547 p 2869JkgK26 273K m3 c Appendix C 7 Question 3 i Relate air velocity to the mass ow rate of air through the nozzle 1 Begin with the mass ow rate equation rh pAv 2 Solve for velocity rh v 7 pA d Appendix D 7 Question 4 i Create a calibration curve to relate the reaction force to the beam de ection Reaction Force vs De ection y 382392 Reaction Foce N 0000 0020 0040 0080 0060 De ection m 0100 012 e Appendix E 7 Spreadsheet Calculations Mass Force De ection Mass Force De ection Mass Flow Rate De ection Predicted Experimental in Force N Force N Air Velocity ms oo Discrepancy Conservation of Energy by Dan Schwarz School of Engineering Grand Valley State University EGR 365 7 Fluid Mechanics Section 01 Instructor Dr S Fleischmann June 5 2007 Outline Purpose Statement a Bemoulli s equation was used to describe the conservation of energy for gravity driven uid ow b The accuracy of Bemoulli s equation was determined through experimentation Background a The experimental system shown in Figure 1 produces a ow of water that is driven by gravity ld DI d1105625in 39 y 875in Figure 1 The experimental system exempli es gravity driven uid flow Fquot Bemoulli s equation can be used to describe the uid ow of this system and kinematics can be used to describe the path of the uid stream The horizontal range of the uid stream is described by Equation 1 See Appendix A for details x2hiyyoi 1 Experimental Method i The tank was lled with water ii A long strip of tape was placed on the side of the tank with depth marks every 2 inches The pressure head at each mark was determined by adding the distance between bottom of the tank and the nozzle to the depth of tank at the mark iii A ruler was placed directly beneath the nozzle to measure the range of the water stream A plumb bob was used to align the ruler O iv The range of the water stream was measured with the ruler each time the water height in the tank was level with one of the 2 inch markings on the tape V Range and pressure head measurements were recorded at 6 different marks III Results Discussion a The measurements taken from the experimental procedure are compared with the predicted ranges in Table l The actual range of the water stream was lower than the predicted range because of energy losses sustained in the nozzle The large discrepancies indicate that the energy loss in the nozzle was very large Hieght h in Actual Range Predicted x x Discrepancy Fquot The range of the water stream was plotted as a function of the pressure head in Figure l The gure indicates that the actual and predicted data trends are approximately parallel The large vertical shift between the data trends is due to the energy loss from the nozzle which resulted in low experimental ranges vs Pres sure Head 4500 4000 3500 a 3000 6 Actual in 2500 Range 34 2000 l Predicted I Range 1500 1000 500 35 37 39 41 43 45 47 49 51 53 55 Pressure Head in Figure 2 Range of the water stream as a function of pressure head IV Conclusions a The main source of experimental error was caused by the oscillating spray of the water stream However the spray of the water stream was not significant enough to account for the large discrepancies as shown by the error bars in Figure 2 b There was no propagated error in this experiment since the range and pressure head measurements were taken directly The large discrepancy was caused by energy losses in the nozzle These losses reduced the kinetic energy of the exiting water which reduced the actual range signi cantly V Appendices a Appendix A 7 Question 1 i Find the range equation when initial velocity is negligible 1 Begin with Bernoulli s equation 1 l 7vl2 gz1 amp7vz2 gz2 p 2 p 2 O 2 If the diameter of the tank is large relative to the diameter of the nozzle then the velocity of the water in the tank is negligible compared to the velocity of the water exiting the tank The static pressure of the water is the same at any point in the system Cancel inappropriate terms gzl EV gzz 3 Rearrange the equation to solve for the initial velocity of the water stream exiting the tank v2 v2 2ng1 22 l l2gh 4 The path of the water stream can be described in the x and y directions using kinematic equations x vzt x0 l t2 y 2 g yo 5 Rearrange the vertical kinematic equation to solve for time t t Z 2 y yo g 6 Substitute the initial velocity of the stream step 3 into the kinematic equation for horizontal range step 4 Also substitute the time equation step 5 into the horizontal range equation For simplicity set the origin of the coordinate system at the origin of the water stream 2 x 2gh imj02lhly yol g ii Find the range equation when initial velocity is not negligible 1 Begin with the conservation of mass equation pV1A1 szA2 2 Substitute the relationship A 761 2 4 into the conservation of mass equation and cancel any redundant terms Vldlz VZdZZ E Rearrange the equation to solve for the velocity of water in the tank v1 2 d Hg 1 4 Substitute this equation in the Bernoulli equation and cancel inappropriate terms 1 EVi A g21 5quot gzz V39 Rearrange the equation to solve for the initial velocity of the water stream exiting the tank v2 2gh v2 1 4 The path of the water stream can be described in the x and y directions using kinematic equations x vzt x0 0 1 2 y5gt y0 gt1 Rearrange the vertical kinematic equation to solve for time t 2 y y 0 g Substitute the initial velocity of the stream step 5 into the kinematic equation for horizontal range step 6 Also substitute the time equation step 7 into the horizontal range equation For simplicity set the origin of the coordinate system at the origin of the water stream Zgh Zyyo 02 hyyo x Vll W g HI b Appendix B 7 Question 2 i Determine if is small enough to consider the velocity of water in the 1 9 tank negligible 1 Find for the system d 39 i 002367 d 10562517 1 2 Find 1 for the system 1 1 0023674 09999 n 1 3 is small enough to consider the velocity of water in the tank negligible c Appendix C 7 Question 3 i Identify the variables in Equation 1 l The dependant variable is the range of the water stream x Hydrostatic Forces by Dan Schwarz School of Engineering Grand Valley State University EGR 365 7 Fluid Mechanics Section 01 Instructor Dr S Fleischmann May 22 2006 m 1 Purpose Statement A Experimentally determine the hydrostatic forces on a submerged planar surface B Compare experimental results to theoretical predictions 11 Background A The pressure variations within a volume of uid can be described by Euler s equation pa g 7 VP 1 B From Euler s equation it was determined that pressure varies linearly in a static body of water open to the atrnosp ere 122 12m gz 2 C In this experiment an inclined hinged door will be subjected to a hydrostatic load until it opens The experimental device is shown below D Two opposing moment equations were developed to determine when the door would open Details in appendix 1 Closing moments gravity amp string tension M RT sin62 05L mg sin61 3 2 Opening moment hydrostatic force of rising water M 05pgwd2kcos61 d3cos261 4 3 These two equations were set equal to each other to predict water depth as a function of tension depth was predicted by nding the roots of the resulting polynomial E Experimental Method 1 Measure all dimensions and angles shown in the gure with a ruler mm and protractor degrees 2 Measure a mass kg record the measurement and hang it from the pulley 3 Place a strip of tape on the side of the tank 4 Slowly ll the tank with water and mark the water level when it reaches the bottom of the door 5 Continue lling the tank with water and mark the water level as soon as the door opens 6 Measure the difference between the initial mark and the nal mark and record the measurement 7 Repeat this method for several masses III Results Discussion A The measurements taken from the experimental procedure are compared with the predicted water levels in the table below Discrepancies were initially high because the water levels did not change much before the door opened Tension Predicted Water Measured Water eve Mass kg B Water depth was plotted as a function of tension in the gure below The gure seems to indicate that the predicted depths were less than the measured depths by the same amount There may have been more moments and forces that where unaccounted for in the prediction Depth vs Tension 010 l a 39 Measmed V Depth 2 a 0 06 Q I Predicted Depth 0 04 002 Te3nsi0n 6N 5 6 7 IV Conclusions A Discrepancies were most likely caused by measurement error when measuring the water depth meniscus reaction time etc B Discrepancies may also result from forces not accounted for in the equations such as friction in the hinges V Appendices A Appendix A 7 Derive Working Equations 1 Closing Moment Equation a Determine moment caused by the weight acting on the centroid of the door 05L mg sin61 b Determine moment caused by the tension force on the door RT sin6 2 c Sum the closing moments M RT sin62 05L mg sin61 3 2 Opening Moment Equation a Setup generic moment integral M J39rPdA b Write r in terms of the variable s I Z rL y L 7 2L S 3 ych 6613 2 c Write P in terms of the variable s P pgscoslt61 d Write dA in terms of the variable s dA wds e Substitute r P and dA into the integral 2 s Mj L a gws cos61ds f Integrate with respect to s 1 s3 3 M ESZL pgwcos61 g Substitute s dcos61 and rearrange the results M 05pgwd2kcos61 d3cos261 4 B Appendix B 7 Assigned Design Calculation 1 The tension needed to hold the door shut with the water level at the hinges was determined to be 143726 N 14651 kg using the equation T 25521076al3 10813674612 02774 C Appendix C 7 Assigned Design Questions 1 Loosening the hinge pins on the door would reduce the friction moment created on the door Since the hinge friction was not accounted for in the working equation reducing the friction would decrease the discrepancy

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

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

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "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."

### 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

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.