S1: Absolute pressure is gauge pressure plus atmospheric pressure.
S2: Gauge pressure is measured by considering absolute zero pressure as datum.
S3: Absolute pressure is measured by considering atmospheric pressure as datum.
S4: Vacuum pressure is negative pressure obtained by subtracting absolute pressure from atmospheric pressure.
Which ONE of the following options lists all the TRUE statements?
Pressure Measurement Analysis
This solution analyzes the statements regarding pressure measurement in a fluid to identify the correct ones.
Statement S1 Analysis
Statement S1 defines absolute pressure relative to gauge pressure and atmospheric pressure.
- Absolute pressure ($P_{abs}$) is the total pressure measured from absolute zero pressure.
- Gauge pressure ($P_{gauge}$) is the pressure measured relative to the local atmospheric pressure ($P_{atm}$).
- The relationship is given by: \( P_{abs} = P_{gauge} + P_{atm} \).
Therefore, Statement S1 is TRUE.
Statement S2 Analysis
Statement S2 describes the datum used for measuring gauge pressure.
- Gauge pressure is measured with atmospheric pressure as the reference (datum).
- Absolute zero pressure is the datum for absolute pressure, not gauge pressure.
Therefore, Statement S2 is FALSE.
Statement S3 Analysis
Statement S3 describes the datum used for measuring absolute pressure.
- Absolute pressure is measured relative to absolute zero pressure.
- Atmospheric pressure is the datum for gauge pressure, not absolute pressure.
Therefore, Statement S3 is FALSE.
Statement S4 Analysis
Statement S4 defines vacuum pressure.
- Vacuum pressure is the pressure below atmospheric pressure. It is essentially negative gauge pressure.
- Mathematically, if $P_{abs} < P_{atm}$, then $P_{gauge} = P_{abs} - P_{atm}$ is negative.
- Vacuum Pressure ($P_{vac}$) can be expressed as $P_{vac} = P_{atm} - P_{abs}$. This is equivalent to $P_{vac} = -P_{gauge}$.
Therefore, Statement S4 is TRUE.
Conclusion
Based on the analysis, statements S1 and S4 are true.
The option listing only the true statements S1 and S4 is Option C.
Important Questions from Hydrostatic Pressure
A cylindrical roller gate of diameter 6.0 m and length 10.0 m is placed on a dam to store water behind it, as shown in figure.
The magnitude of the resultant force due to water acting on that gate when the water is about to spill is _______ $\times 10^6$ N (rounded off to two decimal places).
Consider acceleration due to gravity ($g$) = 9.81 m/s$^2$;
density of water ($\rho$) = 1000 kg/m$^3$; and $\pi$ = 3.14.
With reference to the gate shown in the figure, the gate will start opening automatically when the water level ‘h' above the hinge is _________ m (rounded off to 2 decimal places).
- Two ends of a differential mercury manometer are connected at two points on a pipe carrying oil. The manometer shows difference in mercury level of $20$ cm. The specific gravity of oil and mercury are $0.8$ and $13.6$, respectively. The density of water is $1000$ kg m$^{-3}$ at $4$ °C and acceleration due to gravity (g) is $9.81$ m s$^{-2}$. At the same two points in pipe, the difference of pressure in N m$^{-2}$ is
A plunger weighing 314 kN is balanced in a cylindrical vessel of diameter 1.5 m and filled with an oil (specific gravity 0.9) as shown in the following figure (not to the scale).
If a pressure gauge is connected with the vessel using 1.5 cm diameter tube, the reading of the gauge will be ________ (in kPa, rounded off to two decimal places).
