Concept explainers
The gauge and absolute pressures in the balloon and the peanut jar.
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Answer to Problem 29PE
For Balloon,
Gauge pressure,
Absolute pressure,
For Jar,
Gauge pressure,
Absolute pressure,
Explanation of Solution
Given info:
The manometer along balloon and jar is shown below:
Height of the liquid inside the pipe,
Density of water,
Density of mercury,
Formula used:
Gauge pressure is defined as,
Here,
Absolute pressure is defined as,
Here,
Calculation:
For balloon,
Gauge pressure In the figure (b), it is seen that the pressure inside the balloon is greater than the atmospheric pressure. Since, water is filled inside the pipe to the height
Gauge pressure would be equal to the pressure of the water up to
Absolute pressure,
Substitute the value of
Pressure in terms of height can be written as,
Now, substitute the value of
For Jar,
Gauge pressure From the figure (c), it is seen that pressure inside the jar is lower than the atmospheric pressure. So, gauge pressure would be negative inside the jar.
Mercury is filled inside the pipe. So, gauge pressure would be equal to the pressure of mercury to the height of
Gauge pressure could be written as,
Absolute pressure,
Substitute the value of
Pressure in terms of height of water can be written as,
Now, substitute the value of
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