a tank 2m high is half filled with water and then filled to the top with oil of density 0.8 g/cc . what is the pressure at the bottom of the tank? g= 10m/s2
To find the pressure at the bottom of the tank, we need to consider the pressure due to both the water and the oil.
First, let's calculate the pressure due to the water. The pressure at a certain depth in a fluid is given by the equation:
P = ρgh
Where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.
Given that the tank is 2m high and half-filled with water, the water column has a height of 1m. The density of water is 1000 kg/m³.
So, the pressure due to the water can be calculated as:
P_water = ρ_water * g * h
= 1000 kg/m³ * 10 m/s² * 1 m
= 10,000 Pa
Now, let's calculate the pressure due to the oil. Since the oil is on top of the water, we need to consider the total height of the fluid column.
The remaining height in the tank is also 1m, as the tank is 2m high and half-filled with water. The density of oil is 0.8 g/cc, which is equivalent to 800 kg/m³.
So, the pressure due to the oil can be calculated as:
P_oil = ρ_oil * g * h
= 800 kg/m³ * 10 m/s² * 1 m
= 8,000 Pa
Now, to find the total pressure at the bottom of the tank, we need to add the pressure due to the water and the pressure due to the oil:
P_total = P_water + P_oil
= 10,000 Pa + 8,000 Pa
= 18,000 Pa
Therefore, the pressure at the bottom of the tank is 18,000 Pa.