/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 65 In the United States, gas and li... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 65

In the United States, gas and liquid flow rates are commonly expressed in cubic feet per minute (CFM) and gallons per minute (GPM), respectively. (i) For air at \(1 \mathrm{~atm}\) and \(300 \mathrm{~K}\left(\rho=1.177 \mathrm{~kg} / \mathrm{m}^{3}\right)\), prepare a table showing flow rates in \(\mathrm{m}^{3} / \mathrm{s}\) and \(\mathrm{kg} / \mathrm{s}\) corresponding to \(1,10,100,1000\), and 10,000 CFM. (ii) For water at \(300 \mathrm{~K}\left(\rho=996 \mathrm{~kg} / \mathrm{m}^{3}\right)\), prepare a table showing flow rates in \(\mathrm{m}^{3} / \mathrm{s}\) and \(\mathrm{kg} / \mathrm{s}\) corresponding to \(1,10,100,1000\), and \(10,000 \mathrm{GPM}\).

Short Answer

Expert verified
Air flow rates and water flow rates converted to m鲁/s and kg/s for 1, 10, 100, 1000, and 10,000 CFM and GPM, respectively, are tabulated.

Step by step solution

01

Convert CFM to Cubic Meters per Second

To convert from cubic feet per minute (CFM) to cubic meters per second (m鲁/s), use the conversion factor: 1 CFM = 0.00047194745 m鲁/s. So, for each given CFM value (1, 10, 100, 1000, 10000), multiply by this factor. For example, for 1 CFM:\[1 \text{ CFM} = 1 \times 0.00047194745 \text{ m}^3/\text{s} = 0.00047194745 \text{ m}^3/\text{s}\]
02

Calculate Air Flow Rates in Kg per Second

Given the density of air \( \rho = 1.177 \text{ kg/m}^3 \), multiply the flow rate in m鲁/s by the density to find the mass flow rate in kg/s. For example, for 1 CFM:\[0.00047194745 \text{ m}^3/\text{s} \times 1.177 \text{ kg/m}^3 = 0.0005551356 \text{ kg/s}\]
03

Convert GPM to Cubic Meters per Second

To convert from gallons per minute (GPM) to cubic meters per second (m鲁/s), use the conversion factor:1 GPM = 0.0000630901964 m鲁/s. Apply this factor for each given GPM value (1, 10, 100, 1000, 10000). For instance, for 1 GPM:\[1 \text{ GPM} = 1 \times 0.0000630901964 \text{ m}^3/\text{s} = 0.0000630901964 \text{ m}^3/\text{s}\]
04

Calculate Water Flow Rates in Kg per Second

Given the density of water \( \rho = 996 \text{ kg/m}^3 \), multiply the flow rate in m鲁/s by the density to get the mass flow rate in kg/s. For example, for 1 GPM:\[0.0000630901964 \text{ m}^3/\text{s} \times 996 \text{ kg/m}^3 = 0.0628643961 \text{ kg/s}\]
05

Prepare the Air Flow Rate Table

Create a table listing the flow rates from CFM to m鲁/s and kg/s for air. Use the values calculated in Steps 1 and 2: | CFM | m鲁/s | kg/s | |-----|-------------|------------| | 1 | 0.000471947 | 0.000555 | | 10 | 0.004719475 | 0.005551 | | 100 | 0.047194745 | 0.055514 | | 1000| 0.47194745 | 0.555135 | | 10000| 4.7194745 | 5.551356 |
06

Prepare the Water Flow Rate Table

Create a table listing the flow rates from GPM to m鲁/s and kg/s for water. Use the values calculated in Steps 3 and 4: | GPM | m鲁/s | kg/s | |-----|---------------|------------| | 1 | 0.00006309 | 0.062864 | | 10 | 0.00063090196 | 0.628644 | | 100 | 0.0063090196 | 6.286444 | | 1000| 0.063090196 | 62.864436 | | 10000| 0.63090196 | 628.644366 |

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Cubic Meters Per Second
Cubic meters per second, abbreviated as m鲁/s, is a unit of volumetric flow rate. This unit represents how much volume of a substance, such as air or water, moves through a space per second. It's a metric unit, making it widely used in scientific and engineering contexts.
Understanding this unit is crucial when converting flow rates from units like cubic feet per minute (CFM) or gallons per minute (GPM) to the metric system. For example, 1 cubic foot per minute is equivalent to approximately 0.00047194745 m鲁/s.
Cubic meters per second provide a clear and standard way of expressing flow velocity over cubic feet or gallons, which are uncommon outside the United States. Factoring metric flow rates helps engineers and scientists maintain consistency and precision in their calculations.
Mass Flow Rate
Mass flow rate measures the quantity of mass moving through a given area over time and is often expressed in kilograms per second (kg/s). This is particularly important for understanding the movement of substances in various fields like fluid dynamics and engineering.
To calculate the mass flow rate, you'll need the volumetric flow rate in m鲁/s and the density of the fluid. The formula is straightforward: multiply the flow rate (m鲁/s) by the density (kg/m鲁). This conversion helps in practical applications like designing HVAC systems or assessing water supply in pipelines.
For instance, if air has a flow rate of 0.00047194745 m鲁/s with a density of 1.177 kg/m鲁, the mass flow rate is 0.0005551356 kg/s. This calculation ensures efficiency and accuracy in engineering processes.
Density Conversion
Density is the measure of mass per unit volume of a substance, often given in kilograms per cubic meter (kg/m鲁). When converting flow rates between volume and mass, understanding the density of the fluid is key. It ensures that you convert not just the volume flow rate, but also understand how much mass is moving.
For example, in water, with a density of 996 kg/m鲁, a flow rate of 0.0000630901964 m鲁/s translates into 0.0628643961 kg/s. In air, the density might be much lower, around 1.177 kg/m鲁, altering the mass flow rate greatly compared to water. Problems involving density conversion require precision since physical properties and thermodynamic conditions affect density values.
Accurate density measurements or estimates ensure that the resulting engineering calculations and designs operate under correct assumptions.
Unit Conversion Steps
Unit conversion is a systematic approach in which units are changed from one set to another based on known conversion factors. This is vital in areas where units like CFM and GPM need to be translated into more universally recognized units like m鲁/s or kg/s.
Here's a basic guide to the unit conversion steps:
  • Identify the starting unit and the desired target unit. For instance, CFM to m鲁/s.
  • Find or know the conversion factor, such as 1 CFM = 0.00047194745 m鲁/s.
  • Multiply the original value by the conversion factor to achieve the new unit.
  • If required, convert the flow rate from volume (m鲁/s) to mass (kg/s) by using the density of the substance (kg/m鲁).
Precision in each step is crucial. Errors in unit conversion can lead to significant discrepancies in calculations. Hence, maintaining accuracy in these conversions directly affects the efficiency and safety of engineering designs.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A natural convection heat transfer coefficient meter is intended for situations where the air temperature \(T_{e}\) is known but the surrounding surfaces are at an unknown temperature \(T_{w}\). The two sensors that make up the meter each have a surface area of \(1 \mathrm{~cm}^{2}\), one has a surface coating of emittance \(\varepsilon_{1}=0.9\), and the other has an emittance of \(\varepsilon_{2}=0.1\). The rear surface of the sensors is well insulated. When \(T_{e}=300 \mathrm{~K}\) and the test surface is at \(320 \mathrm{~K}\), the power inputs required to maintain the sensor surfaces at \(320 \mathrm{~K}\) are \(\dot{Q}_{1}=21.7 \mathrm{~mW}\) and \(\dot{Q}_{2}=8.28 \mathrm{~mW}\). Determine the heat transfer coefficient at the meter location.

Suprathane, manufactured by Rubicon Chemicals Inc., is a wall insulation consisting of a sandwich of urethane foam covered with a protective layer on either side. Each protective layer is a composite of aluminum foil over kraft paper interlaced with high-strength glass fiber. For a \(11 / 4\) in-thick sandwich, the \(\mathrm{R}\) value is \(13.2\left[\mathrm{Btu} / \mathrm{hr} \mathrm{ft}^{2}{ }^{\circ} \mathrm{F}\right]^{-1}\). When used in conjunction with a conventional \(31 / 2\) in-thick mineral wool blanket, a wall with a combined \(R\) value of \(22.7\) is claimed. (i) What is the thermal resistance per unit area of the sandwich in SI units? (ii) If inside and outside heat transfer coefficients are estimated to be \(7 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\) and \(20 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\), respectively, what is the rate of heat loss through a \(5 \mathrm{~m}\)-long, \(3 \mathrm{~m}\)-high wall when the inside temperature is \(20^{\circ} \mathrm{C}\) and the outside temperature is \(-20^{\circ} \mathrm{C}\) ?

In a materials-processing experiment on a space station, a \(1 \mathrm{~cm}-\) diameter sphere of alloy is to be cooled from \(600 \mathrm{~K}\) to \(400 \mathrm{~K}\). The sphere is suspended in a test chamber by three jets of nitrogen at \(300 \mathrm{~K}\). The convective heat transfer coefficient between the jets and the sphere is estimated to be \(180 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\). Calculate the time required for the cooling process and the minimum quenching rate. Take the alloy density to be \(\rho=14,000 \mathrm{~kg} / \mathrm{m}^{3}\), specific heat \(c=140 \mathrm{~J} / \mathrm{kg} \mathrm{K}\), and thermal conductivity \(k=240 \mathrm{~W} / \mathrm{m} \mathrm{K}\). Since the emittance of the alloy is very small, the radiation contribution to heat loss can be ignored.

A thermocouple junction bead is modeled as a \(1 \mathrm{~mm}\)-diameter lead sphere \(\left(\rho=11,340 \mathrm{~kg} / \mathrm{m}^{3}, c=129 \mathrm{~J} / \mathrm{kg} \mathrm{K}\right)\) and is initially at a room temperature of \(20^{\circ} \mathrm{C}\). If the thermocouple is suddenly immersed in ice water to serve as a reference junction, what will be the error in indicated temperature corresponding to 1,2, and 3 times the time constant of the thermocouple? If the heat transfer coefficient is calculated to be \(2140 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\), what are the corresponding times?

The thermal resistance per unit area of clothing is often expressed in the unit clo, where \(1 \mathrm{clo}=0.88 \mathrm{ft}^{2}{ }^{\circ} \mathrm{F} \mathrm{hr} / \mathrm{B}\) tu. (i) What is 1 clo in SI units? (ii) If a wool sweater is \(2 \mathrm{~mm}\) thick and has a thermal conductivity of \(0.05 \mathrm{~W} / \mathrm{m}\) \(\mathrm{K}\), what is its thermal resistance in clos? (iii) A cotton shirt has a thermal resistance of \(0.5 \mathrm{clo}\). If the inner and outer surfaces are at \(31^{\circ} \mathrm{C}\) and \(28^{\circ} \mathrm{C}\), respectively, what is the rate of heat loss per unit area?
See all solutions

Recommended explanations on Physics Textbooks

Quantum Physics

Read Explanation

Kinematics Physics

Read Explanation

Electromagnetism

Read Explanation

Atoms and Radioactivity

Read Explanation

Engineering Physics

Read Explanation

Wave Optics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.