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Chapter 9: Problem 21

The gauge pressure of the air in an automobile tire is 32 lb/in \(^{2}\). Convert this to (a) \(\mathrm{Pa},\) (b) torr, \((\mathrm{c})\) atm.

Short Answer

Expert verified
Answer: The equivalent pressure values for 32 lb/in² gauge pressure are approximately 322058.092 Pa, 2415.68 torr, and 3.178 atm.

Step by step solution

01

Convert gauge pressure to absolute pressure

Since atmospheric pressure is approximately 14.7 lb/in², and the given pressure is gauge pressure, to find the absolute pressure, we need to add atmospheric pressure to the gauge pressure. Absolute Pressure = Gauge Pressure + Atmospheric Pressure Absolute Pressure = 32 lb/in² + 14.7 lb/in² Absolute Pressure = 46.7 lb/in²
02

Convert from lb/in² to Pa (Pascal)

To convert from lb/in² to Pa, we will use the following conversion factor: 1 lb/in² = 6894.76 Pa. Absolute Pressure in Pa = Absolute Pressure in lb/in² × conversion factor Pressure in Pa = 46.7 lb/in² * 6894.76 Pa Pressure in Pa = 322058.092 Pa
03

Convert from lb/in² to torr

To convert from lb/in² to torr, we first need to convert from lb/in² to atm, and then from atm to torr using the following conversion factors: 1 lb/in² = 0.06804596 atm 1 atm = 760 torr Absolute Pressure in atm = Absolute Pressure in lb/in² × conversion factor Pressure in atm = 46.7 lb/in² * 0.06804596 atm Pressure in atm ≈ 3.178 atm Now, convert to torr: Pressure in torr = Pressure in atm × conversion factor Pressure in torr = 3.178 atm * 760 torr Pressure in torr ≈ 2415.68 torr
04

Convert from lb/in² to atm (atmosphere)

We have already found the conversion of lb/in² to atm in step 3. Pressure in atm ≈ 3.178 atm
05

Presenting the final results

The pressure in different units is: (a) Pa: 322058.092 Pa (b) torr: 2415.68 torr (c) atm: 3.178 atm

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Most popular questions from this chapter

(a) since the flow rate is proportional to the pressure difference, show that Poiseuille's law can be written in the form \(\Delta P=I R,\) where \(I\) is the volume flow rate and \(R\) is a constant of proportionality called the fluid flow resistance. (Written this way, Poiseuille's law is analogous to Ohm's law for electric current to be studied in Chapter \(18: \Delta V=I R,\) where \(\Delta V\) is the potential drop across a conductor, \(I\) is the electric current flowing through the conductor, and \(R\) is the electrical resistance of the conductor.) (b) Find \(R\) in terms of the viscosity of the fluid and the length and radius of the pipe.
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