A U-shaped tube, open to the air on both ends, contains mercury. Water is poured into the left arm until the water column is deep. How far upward from its initial position does the mercury in the right arm rise?
The rise in the level of the mercury in the right arm, from its initial position is
We know that water and mercury are liquids that are both incompressible and immiscible.
The diagram which can support the fact is given below :
As we know that the water floats on top of the mercury in the left arm, pushing it down from its initial position.
This will happen because the mercury levels are identical at the point and in the figure, the pressure at the point and in the figure must be equal.
Hence, we can say that if the pressures at the sites and are not equal, the fluid will flow in a way that violates the static equilibrium requirement.
In the figure, the pressure at the point is due to water having depth of .
Here, is the atmospheric pressure is the pressure at point , is the density of the water, is the acceleration,
due to gravity, and is the depth of water.
Because mercury is an incompressible fluid, it will travel down a distance in the left arm while travelling up a distance in the right arm.
This implies that the pressure at point is due to the mercury having a depth of .
Now, we can see that the pressure at point is
In the above expression here, is the atmospheric pressure is the pressure at point , is the density of the mercury. is the acceleration due to gravity, and is the depth of mercury.
Equate the equation and
Rearrange the above equation in terms of
Substitute for , for , for
The temperature in the right arm has increased from its original
a. A liquid of density flows at speed through a horizontal pipe that expands smoothly from diameter to a larger diameter . The pressure in the narrower section is . Find an expression for the pressure in the wider section.
b. A pressure gauge reads as water flows at through a -diameter horizontal pipe. What is the reading of a pressure gauge after the pipe has expanded to in diameter?
Astronauts visiting a new planet find a lake filled with an unknown liquid. They have with them a plastic cube, on each side, with a density of . First they weigh the cube with a spring scale, measuring a weight of . Then they float the cube in the lake and find that two-thirds of the cube is submerged. At what depth in the lake will the pressure be twice the atmospheric pressure of ?
94% of StudySmarter users get better grades.Sign up for free