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Chapter 1: Problem 24

\( The absolute pressure inside a tank is \)0.4\( bar, and the surrounding atmospheric pressure is \)98 \mathrm{kPa}\(. What reading would a Bourdon gage mounted in the tank wall give, in \)\mathrm{kPa} ?$ Is this a gage or vacuum reading?

Short Answer

Expert verified
The Bourdon gage would show a vacuum reading of 58 kPa.

Step by step solution

01

Convert the absolute pressure to kPa

First, convert the given absolute pressure in the tank from bar to kilopascals (kPa). We know that 1 bar = 100 kPa. Therefore, the absolute pressure inside the tank is 0.4 bar * 100 kPa/bar = 40 kPa.
02

Identify the atmospheric pressure

The surrounding atmospheric pressure is given as 98 kPa.
03

Calculate the gage pressure

The gage pressure can be found by subtracting the atmospheric pressure from the absolute pressure: \[ P_{gage} = P_{absolute} - P_{atmosphere} \] Substitute the known values: \[ P_{gage} = 40 \text{kPa} - 98 \text{kPa} = -58 \text{kPa} \]
04

Interpret the result

A negative gage pressure indicates a vacuum reading. Therefore, the Bourdon gage would show a vacuum pressure of 58 kPa.

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Key Concepts

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

absolute pressure
Absolute pressure is the total pressure within a closed system, measured relative to a perfect vacuum. In other words, it鈥檚 the pressure of a system plus the atmospheric pressure acting on it.
For example, if a tank has an absolute pressure of 0.4 bar, this includes both the pressure inside the tank and the atmospheric pressure pressing down on it. One bar is equal to 100 kPa, so 0.4 bar is equivalent to 40 kPa.
Understanding absolute pressure is crucial because it helps determine the actual force exerted inside the system, without omitting the influence of atmospheric pressure.
atmospheric pressure
Atmospheric pressure is the pressure exerted by the weight of the air above us. It varies with altitude and weather conditions, but at sea level, it's approximately 101.3 kPa or 1 atmosphere (atm).
In our exercise, the atmospheric pressure is given as 98 kPa. This means that the pressure exerted by the air around the tank is 98 kPa. When we measure other pressures, we often use atmospheric pressure as a reference point.
It's essential to keep in mind that atmospheric pressure can influence readings of other types of pressure, such as gauge and vacuum pressures.
gauge pressure
Gauge pressure is the pressure relative to the atmospheric pressure. It can be positive or negative, depending on if the system's pressure is greater or less than atmospheric pressure.
In our exercise, we calculated the gauge pressure using the formula:
\[ P_{\text{gage}} = P_{\text{absolute}} - P_{\text{atmosphere}} \]
By plugging in our values, we find:
\[ P_{\text{gage}} = 40 \text{kPa} - 98 \text{kPa} = -58 \text{kPa} \]
A negative gauge pressure means the pressure inside the tank is less than the surrounding atmospheric pressure. This negative value often indicates a vacuum or partial vacuum.
vacuum reading
A vacuum reading is observed when the pressure inside a system is lower than the surrounding atmospheric pressure. It is often represented as a negative gauge pressure.
In our problem, we determined that the tank's gauge pressure is -58 kPa. This negative value indicates a vacuum reading, meaning the pressure inside the tank is 58 kPa less than the atmospheric pressure of 98 kPa.
Understanding vacuum pressure is important in many applications, such as in vacuum packaging, industrial processes, and scientific experiments where controlling the environment is crucial.

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Most popular questions from this chapter

Water is the working fluid in an ideal Rankine cycle with reheat. Superheated vapor enters the turbine at \(8 \mathrm{MPa}\), \(440^{\circ} \mathrm{C}\), and the condenser pressure is \(8 \mathrm{kPa}\). Steam expands through the first- stage turbine to \(0.5 \mathrm{MPa}\) and then is reheated to \(440^{\circ} \mathrm{C}\). Determine for the cycle (a) the rate of heat addition, in \(\mathrm{kJ}\) per \(\mathrm{kg}\) of steam entering the first-stage turbine. (b) the thermal efficiency. (c) the rate of heat transfer from the working fluid passing through the condenser to the cooling water, in kJ per \(\mathrm{kg}\) of steam entering the first-stage turbine.

A gas initially at \(p_{1}=1\) bar and occupying a volume of 1 liter is compressed within a piston-cylinder assembly to a final pressure \(p_{2}=4\) bar. (a) If the relationship between pressure and volume during the compression is \(p V=\) constant, determine the volume, in liters, at a pressure of 3 bar. Also plot the overall process on a graph of pressure versus volume. (b) Repeat for a linear pressure-volume relationship between the same end states.

In a steam power plant working on Rankine cycle, superheated steam enters the steam turbine at 20 bar, \(400^{\circ} \mathrm{C}\) and exits it at \(0.08\) bar. It then enters the condenser, where it is condensed to saturated liquid water at \(0.08\) bar. The mass flow rate of the steam is \(50 \mathrm{~kg} / \mathrm{s}\). If both turbine and pump have an efficiency of \(85 \%\) each, determine the rate of exergy input to the working fluid, in MW passing through the steam generator. Let \(T_{0}=293 \mathrm{~K}\) and \(p_{0}=1\) bar.

Water is used as the working fluid in an ideal Rankine cycle with reheat. At the inlet to the first-stage turbine the conditions are \(14 \mathrm{MPa}, 580^{\circ} \mathrm{C}\), and the steam is reheated between the turbine stages to \(580^{\circ} \mathrm{C}\). For a reheat pressure of \(7 \mathrm{MPa}\), plot the cycle thermal efficiency versus condenser pressure for pressures ranging from \(4 \mathrm{kPa}\) to \(100 \mathrm{kPa}\).

The storage tank of a water tower is nearly spherical in shape with a radius of \(9 \mathrm{~m}\). If the density of the water is \(1000 \mathrm{~kg} / \mathrm{m}^{3}\), what is the mass of water stored in the tower, in lb, when the tank is full? What is the weight, in \(\mathrm{N}\), of the water if the local acceleration of gravity is \(9.8 \mathrm{~m} / \mathrm{s}^{2} ?\)
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