Find the pressure at the bottom of a vessel 80cm deep filled with water.
The pressure at the bottom of a vessel filled with water depends on the depth of the water and the density of water. The pressure at any depth is equal to the weight of the liquid above that depth plus the weight of the atmosphere above the liquid.
Assuming that the vessel is open to the atmosphere and the density of water is 1000 kg/m³, the pressure at the bottom of the vessel can be calculated as follows:
1. Convert the depth of the water to meters:
80 cm = 0.8 m
2. Calculate the weight of the water above the bottom of the vessel:
The weight of water is equal to its mass times gravity, which is approximately 9.81 m/s².
The volume of water in the vessel can be calculated using the formula for the volume of a cylinder:
V = πr²h
where V is the volume, r is the radius, and h is the height of the cylinder. Assuming that the vessel is a perfect cylinder with a radius of 1 meter, the volume of water in the vessel is:
V = π(1²)(0.8) = 2.01 m³
The mass of water in the vessel can be calculated using the formula:
m = ρV
where m is the mass, ρ is the density, and V is the volume. Substituting the values:
m = (1000 kg/m³)(2.01 m³) = 2010 kg
So, the weight of the water is:
Wwater = mg = (2010 kg)(9.81 m/s²) = 19732.1 N
3. Calculate the weight of the atmosphere above the liquid:
The weight of the atmosphere can be assumed to be approximately 101325 Pa (pascals) at sea level. To convert this to Newtons per square meter (N/m²), we can use the formula:
1 Pa = 1 N/m²
So, the weight of the atmosphere is:
Watmosphere = 101325 N/m²
4. Calculate the total pressure at the bottom of the vessel:
The total pressure at the bottom of the vessel is the sum of the pressure due to the weight of the water and the pressure due to the weight of the atmosphere.
Ptotal = Pwater + Patmosphere
where:
Pwater = Wwater / A
is the pressure due to the weight of the water, and A is the cross-sectional area of the vessel. Assuming that the vessel is a perfect cylinder with a radius of 1 meter, the area is:
A = πr² = π(1²) = π m²
Substituting the values, we get:
Pwater = (19732.1 N) / (π m²) ≈ 6283.9 N/m²
And,
Ptotal = 6283.9 N/m² + 101325 N/m² ≈ 107609.0 N/m²
Therefore, the pressure at the bottom of the vessel is approximately 107609.0 N/m² or 107609 Pa or 1.0761 bar.
What volume (in cc) will 400g of silver occupy if its density is 10.5 g/ml?
To find the volume occupied by 400g of silver, we can use the formula:
Density = Mass / Volume
Rearranging the formula, we get:
Volume = Mass / Density
Substituting the given values:
Volume = 400g / 10.5 g/ml
Volume = 38.095 cc (rounded to 3 decimal places)
Therefore, 400g of silver will occupy a volume of approximately 38.095 cc if its density is 10.5 g/ml.
To find the pressure at the bottom of a vessel filled with water, you can use the concept of hydrostatic pressure. Hydrostatic pressure is the pressure exerted by a fluid at rest due to the weight of the fluid above.
The formula to calculate hydrostatic pressure is:
P = ρgh
Where:
P = Pressure
ρ = Density of the fluid (Water has a density of approximately 1000 kg/m³)
g = Acceleration due to gravity (approximately 9.8 m/s²)
h = Height or depth of the fluid column
In this case, the height or depth (h) is given as 80 cm, but it needs to be converted to meters by dividing it by 100:
h = 80 cm ÷ 100 = 0.8 m
Now we can calculate the pressure:
P = (1000 kg/m³) x (9.8 m/s²) x (0.8 m)
P ≈ 7840 Pascal
So, the pressure at the bottom of the vessel filled with water is approximately 7840 Pascal.