GATE ME 2016 Set 1 — Question 49
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Fluid Mechanics → Fluid Properties & Statics → Manometry
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Question
An inverted U-tube manometer is used to measure the pressure difference between two pipes A and B, as shown in the figure. Pipe A is carrying oil (specific gravity = 0.8) and pipe B is carrying water. The densities of air and water are and , respectively. The pressure difference between pipes A and B is __________ kPa.Acceleration due to gravity g = 10 m/s.
Correct answer
2.19 to 2.21
Solution
Given:
Wait, let's re-examine the diagram for the inverted U-tube. In an inverted manometer, we subtract the pressure of the fluid columns as we go up:
-- wait, the diagram shows the water column is total if we consider the air-water interface at the top of the section.If we neglect the air density (as it is very small compared to liquids):
Including air density:
The magnitude of the pressure difference is approximately . The official answer key accepts the range to (or to ).
- Specific gravity of oil,
- Density of water,
- Density of air,
- Acceleration due to gravity,
- Height of oil column in the left limb,
- Height of water column in the right limb,
- The air column heights are and .
Wait, let's re-examine the diagram for the inverted U-tube. In an inverted manometer, we subtract the pressure of the fluid columns as we go up:
-- wait, the diagram shows the water column is total if we consider the air-water interface at the top of the section.If we neglect the air density (as it is very small compared to liquids):
Including air density:
The magnitude of the pressure difference is approximately . The official answer key accepts the range to (or to ).
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