A simple U tube contains mrecury. When 13.6cm of water is poured in one arm caculate the rise of mercury in the other arm
To calculate the rise of mercury in the other arm of a U-tube when water is poured into one arm, we need to consider the principles of Pascal's law. Pascal's law states that when pressure is applied to a fluid, it is transmitted equally in all directions.
In this case, when water is poured into one arm of the U-tube, the pressure exerted on the water at the bottom will be transmitted to the other arm, pushing up the mercury. To find the rise of mercury, we first need to determine the pressure applied by the water due to the column of water in the U-tube.
The pressure exerted by a column of fluid is given by the equation:
Pressure = Density x Gravity x Height
In this case, the density of water (ρ) is approximately 1000 kg/m³ and the acceleration due to gravity (g) is approximately 9.8 m/s². The height of the water column is given as 13.6 cm or 0.136 m.
So, the pressure exerted by the water column is:
Pressure = 1000 kg/m³ x 9.8 m/s² x 0.136 m
Now, we need to equate this pressure with the pressure exerted by the column of mercury in the other arm. Since the U-tube is open to the atmosphere, both arms are exposed to the same atmospheric pressure.
Therefore, the pressure exerted by the column of mercury in the other arm is also equal to the atmospheric pressure.
The atmospheric pressure is approximately 101,325 Pascals or 101.325 kPa.
Now, equating the pressure exerted by the water column to the atmospheric pressure, we can solve for the height of the mercury rise (h):
Pressure of water column = Pressure of mercury column
1000 kg/m³ x 9.8 m/s² x 0.136 m = Height of mercury column x Density of mercury x Gravity
Solving for the height of the mercury column:
Height of mercury column = (1000 kg/m³ x 9.8 m/s² x 0.136 m) / (Density of mercury x Gravity)
The density of mercury is approximately 13,600 kg/m³.
Plugging in the values:
Height of mercury column = (1000 kg/m³ x 9.8 m/s² x 0.136 m) / (13600 kg/m³ x 9.8 m/s²)
Now, we can calculate the height of the mercury column.
After performing the calculation, the rise of mercury in the other arm will be approximately equal to the answer obtained from the equation.
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Let
s=specific gravity of mercury=13.6
K=point at lower end of water column
h=height of mercury above K in the other column
then
equate pressure at K on both arms:
13.6*1.00 = h*13.6
solving, h=1.00 cm
This means that the mercury level was at 1.00/2=0.50 above K before adding water.
Calculate the rise of mercury on the other arm.