Calculate the Patm And the pressure exerted by water on the block
- The area Of the upper face of block is 40 cm2 Calculate the total pressure exerted on the solid
Given : In the first tube : in a tube a solid .. the height from solid to the water level in the tube is 8o cm
& in the 2nd tube the height of the solid on the surface of water is 75 cm ( the height of the solid above water )
To calculate the total pressure exerted on the solid, we need to consider the pressure exerted by the atmosphere (Patm) and the pressure exerted by the water on the block.
1. Calculate Patm:
The pressure exerted by the atmosphere, Patm, can be calculated using the following formula:
Patm = ρgh
where ρ is the density of the fluid (air), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the solid above the water level.
Given that the height of the solid above the water level is 75 cm, we first need to convert it to meters:
h = 75 cm = 0.75 m
The density of air is approximately 1.225 kg/m^3.
Substituting the values into the formula:
Patm = 1.225 kg/m^3 * 9.8 m/s^2 * 0.75 m
Patm ≈ 9.06 Pa
So, Patm is approximately 9.06 Pascal.
2. Calculate the pressure exerted by the water:
The pressure exerted by the water on the block can be calculated using the formula:
P = ρgh
where ρ is the density of the fluid (water), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the water column.
Given that the height from the solid to the water level in the first tube is 80 cm and in the second tube is 75 cm, we first need to convert them to meters:
h1 = 80 cm = 0.8 m
h2 = 75 cm = 0.75 m
The density of water is approximately 1000 kg/m^3.
Substituting the values into the formula:
P1 = 1000 kg/m^3 * 9.8 m/s^2 * 0.8 m
P1 ≈ 7840 Pa
P2 = 1000 kg/m^3 * 9.8 m/s^2 * 0.75 m
P2 ≈ 7350 Pa
So, the pressure exerted by the water in the first tube is approximately 7840 Pascal and in the second tube is approximately 7350 Pascal.
3. Calculate the total pressure exerted on the solid:
To calculate the total pressure exerted on the solid, we need to add the pressure exerted by the atmosphere to the pressure exerted by the water:
Total pressure = Patm + Pressure exerted by water
Total pressure in the first tube = 9.06 Pa + 7840 Pa ≈ 7849.06 Pa
Total pressure in the second tube = 9.06 Pa + 7350 Pa ≈ 7359.06 Pa
So, the total pressure exerted on the solid in the first tube is approximately 7849.06 Pascal, and in the second tube is approximately 7359.06 Pascal.
To calculate the total pressure exerted on the solid, we need to consider two components: the atmospheric pressure (Patm) and the pressure exerted by water.
1. Atmospheric Pressure (Patm):
Atmospheric pressure is the pressure exerted by the Earth's atmosphere on a given surface. The average atmospheric pressure at sea level is approximately 101.3 kilopascals (kPa) or 1 atmosphere (atm).
2. Pressure Exerted by Water:
The pressure exerted by water depends on the depth of the water column above the object. We can use the formula P = ρgh, where P is the pressure, ρ is the density of water, g is the acceleration due to gravity, and h is the height of the water column.
First, let's convert the height of the water column from centimeters to meters for both tubes:
- Tube 1: The height of the water column is 80 cm. Converting to meters: h1 = 80 cm / 100 cm = 0.8 m.
- Tube 2: The height of the solid above water is 75 cm. Converting to meters: h2 = 75 cm / 100 cm = 0.75 m.
Now, let's calculate the pressure exerted by water in each tube:
- Tube 1: P1 = ρgh1
- Tube 2: P2 = ρgh2
To calculate the total pressure exerted on the solid, we need to sum the atmospheric pressure and the pressure exerted by water:
Total Pressure = Patm + P1 + P2
To get the final answer, we also need to know the density of water (ρ) and the value of atmospheric pressure (Patm). If these values are not provided, the calculations cannot be completed.