Thermal & Fluids PE Exam Technical Study Guide Errata This product has been updated to incorporate all changes shown in the comments on the webpage and email comments as of October, 30 2017. If you have purchased this product prior to this date and wish for the latest version then please email Justin Kauwale at contact@engproguides.com. August 7, 2018: The following figures were shown as blank. They have been updated as part of the errata and are attached immediately after this errata write-up. Basic Engineering Practice Figures 3 & 4 Fluid Mechanics Figures 5, 6, 7 & 12 Thermodynamics Figure 1 & 2 March 13, 2018: The equation for SCFM and ACFM was incorrect. Please see below for the correct equation. This affected page 7 of Hydraulic and Fluids and Problem 11.2. These pages have been revised and are attached to this PDF. Thermal & Fluids PE Technical Study Guide Errata -1 www.engproguides.com
March 19, 2018: Hydraulic and Fluids Applications, Problem 6, Hydraulics was revised as shown below. March 19, 2018: Energy/Power Applications, All instances of bypass factor and contact factor have been switched as shown below. Coils Bypass Factor h leaving coil h h apparatus de ew point h en ntering coil h apparatus de ew point Contact Factor 1 h leavin ng coil h app aratus dew point h enterin ng coil h app paratus dew point h en ntering coil h leaving coil h enteri ing coil h ap pparatus dew point Thermal & Fluids PE Technical Study Guide Errata -2 www.engproguides.com
Figure 3: A side view or elevation view of the same object, with dimension lines. Figure 4: A side view or elevation view of the same object, with dimension lines. Basic Engineering Practice-6
Air Properties R 53.35 k 1.4 Units ft lbf lbm R N/A Figure 3: Universal gas constant for air. The gas constant willl vary based on the gas. The speed of sound is important because it helps to determine when a fluid is compressible or incompressible. Once the speed of a fluid is out of the incompressible range, then many of the simplified equations used in Thermodynamics andd Fluids cannot be used. Instead, compressible equations must be used. Description Incompressible Sub-sonic Speed of sound Super sonic Mach Number Range 0 to 0.3 0.3 to 1 1 1 to 5 Figure 4: Incompressible fluids have a Mach numberr less than 0.3. On the exam, you should assume incompressible fluid unless told otherwise. 4.2 N NOZZLES Nozzles are used to create changes in velocities and pressures of a moving fluid. A nozzle in its simplest form increases the velocity of a fluid by reducing the area, which also increases the fluids pressure. The nozzle is an important part of the exam and if youu can understand what the fluid is doing through the nozzle, then you will be in a good position too get these types of questions correct. Figure 5: A nozzle increases the pressuree of the fluid, decreases temperaturee and increases the velocity of the fluid. 4.2.1 Conservation n of energy & mass One important concept to understand for both nozzles and diffusers is that energy is assumed to be conserved as the fluid passes throughh the nozzle. Any kinetic energy change (change in velocity) must be accounted for in a change in internal energy. For example, an increase in Fluid Mechanics-1 10
Figure 6: Converging diverging nozzle 4.3 D DIFFUSERSS Diffuserss are the opposite of nozzles. Diffusers decrease the pressure of the fluid by reducing the velocity. Figure 7: A diffuser decreases the pressuree of the fluid, increases temperaturee and decreases the velocity of the fluid. On the exam, use problems. the same equations to solve diffuser problems as you would for nozzle 4.4 B BULK MODULUS The term Bulk Modulus is a property of a fluid that describes the compressibility of the Bulk modulus, β, is defined in the equation below. fluid. β P ;psii V/V In this equation, V is the original volume of the fluid and delta V is the change in volume, when a pressuree change is applied to the fluid. Bulk modulus has units of pressure. Make sure you tab the Bulk Modulus properties in your r MERM. These values will be helpful in determining the change in volume when a pressure iss applied to a fluid. For example, if a hydraulic fluid has a bulk modulus of 200,000 psi and a pressure of 1,000 psi applied to the fluid (V = 10 in 3 ), then the change in volume can be found with the below equation. Fluid Mechanics-1 12
5.5 F FLUID POWER A large portion of the Thermal & Fluids field is using fluids to transmit power in hydraulic and pneumatic industrial systems. Pneumatics is the transfer of energy via compressed air and hydraulics is the transfer of energy via hydraulic fluid like oil. For example, pneumatics is used in the medical field, construction, manufacturing and packaging. Hydraulic fluids are used heavily in the construction and industrial industries too power large equipment like tractors, cranes, excavators, etc. This section of the book provides you a basic understanding of the engineering principles behind both hydraulics and pneumatics. The first principle is Pascal s Law. This law states thatt pressure is transmitted undiminished in all directions and exerts equal force on all areas for a confined fluid at rest. This means that anywheree within a circuit, pipe, pressure vessel, the fluid s pressuree is equal. Also be sure that the fluid is confined at rest. If the fluid is moving, then friction lossess will occur. Figure 12: The pressure acting upon all surfaces by the fluid in pink is equal, in accordance with Pascal s law. p pressure lbs in; F p F A Here are some conversions that you should be familiar with. force lbs; ; A πr 2 area in 2 Pascal (Pa) Megapascal (Mpa) Bar Lbs-sq-in (psi) 1 Pa 1 Mpa 1 Bar 1 Psi 1 10 10 6,895 1 1 0.1 6.895 x 10 10 10 10 1.06895 145.04 x 10 145 14.5 1 Fluid Mechanics-2 22
3.0 THERMODYNAMICS PROPERTIES On the exam, you should be able to find thermodynamic properties very easily through the use of your thermodynamic property tables for given fluids, located in your Mechanical Engineering Reference Manual or Schaum s Thermodynamics for Engineers. These properties are the building blocks for solving the problems on the exam. You should also have a concept of what these properties mean in the real world. These concepts will help to reality check your answers, instead of blindly following the results of your equations. Hopefully, this helps you to catch any math errors and speeds up your elimination of incorrect multiple choice answers. 3.1 PRESSURE Pressure is one of the two most likely properties that you will start off with in a real world situation, because pressure is a thermodynamic property that is easily measured. Figure 1: Pressure gauge The pressure of a fluid indicates the amount of force per unit area that the fluid imparts on the materials around it. Pressure is typically measured in units of pounds per square inch psi. There are two different types of pressure scales, (1) absolute pressure and (2) gauge pressure. These two pressure scales differ by their 0 reference point. Gauge pressures have a 0-reference point as 1 atm. Thus 0 psig, where the g indicates gauge pressure, is equal to 1 atmospheric or 14.7 psia, where the a indicates absolute pressure. Most real world applications encountered by practicing engineers will have pressures indicated in gauge pressure. These include pressures measured at the discharge and intake of pumps and fans and the pressures measured at other pieces of equipment like heat exchangers, chillers and cooling towers. The relationship between gauge and atmospheric pressure is shown with the following equation and figure. P psi P psi 14.7 psi Thermodynamics-9
P 1 atm P 2atm P 0 atm P 1atm P 0atm Figure 2: The relationship between gauge and absolute pressures, gauge pressure on the left and absolute pressure is shown on the right. 3.2 TEMPERATURE Temperature is the second of the two most likely property that you will start off with in a real world situation, because temperature is easy to measure. Figure 3: A temperature gauge. This property is the one most people are familiar with, because it is displayed on thermostats and thermometers. Temperature is a direct indication of the amount of heat in the fluid. The United States Customary Systems (USCS) units used for temperature are Fahrenheit and Rankine. Typical Fahrenheit temperatures for chilled water (medium used for water-cooled air conditioning) range from 45F to 55F and hot water temperatures range from 120F to 140F. The temperature at which water boils is 212F and water freezes at 32F. Rankine temperatures are used when it is necessary to define an absolute temperature scale having only positive values. The conversion between Fahrenheit and Rankine is shown below. When using equations during the exam, ensure that the correct temperature units are used. Always double check the required units for your equation. R 460 The above equation converts Fahrenheit to Rankine. Thermodynamics-10
Coils Thermal & Fluids PE Technical Study Guide Errata -2 www.engproguides.com
8.5 PROBLEM 3: CALCULATE THE REYNOLDS NUMBER 250 gpm of 120F water flows through a 4 diameter pipe that is located in the ceiling of a building. Assume the water in the pipe is not under extreme pressure. Calculate the Reynolds number of the fluid inside the pipe. a) 57,734 b) 295,941 c) 355,745 d) 136,836,344 Heat Transfer-23
8.6 SOLUTION 3: CALCULATE THE REYNOLDS NUMBER The Reynolds number is found by the following equation Where, 4 1 0.33 ft, 12 8.33 250 61.3 1 0.566 60, 0.566 0.33 2 6.5, Use the tables in the MERM or your own resources to find the kinematic viscosity of water at 120F. Because the properties of water do not change drastically under minor pressure differences, water at atmospheric pressure can be used as a close estimate. 0.609 x 10, Solve for Reynolds number: 0.33 6.5 355,775 0.609 x 10 Heat Transfer-24
Fans.,., Fan affinity laws RPM constant Impeller diameter (N) is constant ACFM vs SCFM. ; Hydraulic/Fluid Applications-7
4.5 USING THE AFFINITY LAWS It is often necessary to determine how a pump will operate under differing operating conditions. The operating conditions of a pump that can most readily be changed are the impeller diameter and the rotational speed of the pump. In order to predict how a centrifugal pump will behave prior to changing the speed or the impeller diameter, the engineer can use the affinity laws shown below. The first set of affinity laws is that the flow rate (Q) is directly proportional to the size of the diameter of the pump impeller (D) and/or the rotational speed (N) of the pump. ; ; The second affinity law is that the total head (H) is directly proportional to the square of the size of the diameter of the pump impeller (D) and/or the square of the rotational speed (N) of the pump. ; ; The third affinity law is that the power (P) is directly proportional to the cube of the size of the diameter of the pump impeller (D) and/or the cube of the rotational speed (N) of the pump. ; ; Hydraulic/Fluid Applications-21
4.5.1 Similarity Laws You may come across these formulas, if you encounter a question that compares two similar pumps. These formulas are called the similarity laws. These laws compare similar pumps within the same series of pumps. The previous formulas compared the original condition and new condition of the same pump. These formulas compare two similar pumps, with different diameters. In order to best understand what is meant by same series of pumps, visit a manufacturer s website and you will see various pump series that have varying sizes within the same series. Within a series of pumps, a pump with x diameter impeller and y diameter volute can be compared to another pump in the same series of pumps, but with 2x diameter impeller and 2y diameter volute. The second pump is similar but has twice the diameter of the first pump. = = = = = =. = = =..... 4.6 MULTIPLE PUMPS Pumps and fans can be provided in series or parallel. Please read the section on Multiple Fans for more information. The same concept presented on multiple fans also applies to pumps. 4.7 PIPE DESIGN When designing a piping system for your fluid (chilled water, condenser water, hot water, steam), you must be able to choose the correct material for the application, choose the correct Hydraulic/Fluid Applications-22
5.5 FAN AFFINITY LAWS Often times a fan s speed or impeller diameter will be changed. If the fan is a centrifugal fan, then the change in performance of the fan can be predicted quickly through the affinity laws. First, if the impeller diameter is held constant and the speed of the fan is changed, then flow rate varies directly with the speed, available pressure varies with the square of the speed and the power use varies with the cube of the speed. : Second, if the speed is held constant and the impeller diameter of the fan is changed, then flow rate varies directly with the diameter, available pressure varies with the square of the diameter and the power use varies with the cube of the diameter. : Hydraulic/Fluid Applications-35
5.5.1 Similarity Laws You may come across these formulas, if you encounter a question that compares two similar fans. These formulas are called the similarity laws. These laws compare similar fans within the same series of fans. The previous formulas compared the original condition and new condition of the same fan. These formulas compare two similar fans, with different diameters. In order to best understand what is meant by same series of fans, visit a manufacturer s website and you will see various fan series that have varying sizes within the same series. Within a series of fans, a fan with x diameter wheel and y diameter casing can be compared to another fan in the same series of fans, but with 2x diameter wheel and 2y diameter casing. The second pump is similar but has twice the diameter of the first fan. = = = = = =. = = =..... 5.6 MULTIPLE FANS There will be times when fans are run in conjunction with each other. It is important for the engineer to understand how the performance is affected depending on the different arrangements of multiple fans. Hydraulic/Fluid Applications-36
11.2 SOLUTION 1 PRESSURE VESSEL What is the stress in a cylindrical pressure vessel when the fluid inside of the vessel is at a pressure of 10,000 psi? The vessel is 10 feet long and has a diameter of 4 feet. The vessel is 3 thick. for cylindrical thin walled pressure vessels σ PR t 10,000 psi 4 ft 12 in/ft 2 σ 3 in σ80,000 psi The answer is most nearly, (A), 100,000 psi. Hydraulic/Fluid Applications-57
11.3 PROBLEM 2 ACFM The flow rate of air at standard temperature and pressure is 2000 cfm. What is the flow rate when ambient conditions are 4 psig and 80 o F. (a) 1634 cfm (b) 2447 cfm (c) 2550 cfm (d) 3530 cfm Hydraulic/Fluid Applications-56
11.4 SOLUTION 2 ACFM The flow rate of air at standard temperature and pressure is 2000 cfm. What is the flow rate when ambient conditions are 4 psig and 80 o F. Use the following equation to convert from standard cfm (SCFM) to actual cfm (ACFM). The pressure is given in psig and must first be converted to psia and the temperature must be converted to Rankine. 4 14.7 18.7 80 459.7 539.7 Solve for ACFM. 18.7 519 2000 1,634 14.7 539.7 The answer is (A), 1634 cfm. Hydraulic/Fluid Applications-57
12.0 PRACTICE PROBLEMS 12.1 PROBLEM 1 NET POSITIVE SUCTION HEAD A cooling tower is located such that the fluid level in the basin is 15 ft above the centerline for the suction of the condenser water pump. The water is at an average temperature of 88 F. The friction loss from the cooling tower basin to the suction of the pump is approximately 12 ft of head. What is the net positive suction head available at the suction side of the pump with a flow rate of 320 GPM? (a) 16.3 ft of head (b) 30.9 ft of head (c) 35.6 ft of head (d) 37.0 ft of head Energy/Power Applications-66