A rectangular tank 0.30m × 0.30m × 0.60 m is filled with ethyl alcohol to a full depth of 0.30 the pressure at the surface of the alcohol is 1.013x10⁶ Pa. Find the pressure at the bottom of a tank
Assuming the acceleration due to gravity is 9.81 m/s² and the density of ethyl alcohol is 789 kg/m³, we can use the formula:
pressure = density x gravity x depth
At the surface, the pressure is given as 1.013x10⁶ Pa. The depth is 0.30 m and the density is 789 kg/m³:
1.013x10⁶ = 789 x 9.81 x 0.30
To find the pressure at the bottom of the tank, we need to add the depth of the alcohol to the initial depth:
total depth = 0.30 + 0.30 = 0.60 m
Now we can use the same formula to find the pressure at the bottom:
pressure = density x gravity x depth
pressure = 789 x 9.81 x 0.60
pressure = 4.617x10⁴ Pa
Therefore, the pressure at the bottom of the tank is 4.617x10⁴ Pa.
Well, if we're talking about pressure, it's always good to remember that pressure comes from all sides, like a good group hug. So, let's calculate the pressure at the bottom of the tank.
First, we need to know the height of the ethyl alcohol in the tank. Since the tank is filled to a depth of 0.30m, and the tank itself is 0.60m tall, then the height of the ethyl alcohol is 0.30m.
Now, let's consider a column of ethyl alcohol with a height of 0.30m. The pressure at the bottom of this column is determined by the weight of the liquid above it.
The pressure at any point in a fluid is given by the equation P = ρgh, where P is the pressure, ρ is the density, g is the acceleration due to gravity, and h is the height of the fluid column.
The density of ethyl alcohol is approximately 789 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s². Plugging in these values, we get:
P = (789 kg/m³) * (9.8 m/s²) * (0.30m)
Calculating this gives us:
P = 2,304.18 Pa
So, the pressure at the bottom of the tank is approximately 2,304.18 Pa.
Of course, this is all assuming that the ethyl alcohol isn't doing any funny business down there, like hosting a pressure party or doing some underwater acrobatics. But as far as we know, it should be a nice, straightforward pressure value.
To find the pressure at the bottom of the tank, we can use the concept of hydrostatic pressure.
The hydrostatic pressure at a certain depth within a liquid can be calculated using the formula:
P = ρgh
Where:
P is the pressure at the given depth,
ρ is the density of the liquid,
g is the acceleration due to gravity,
and h is the depth below the liquid surface.
In this case, we can assume that the density of ethyl alcohol is ρ = 789 kg/m³ (at room temperature) and the acceleration due to gravity is g ≈ 9.8 m/s².
Given that the tank is filled to a depth of h = 0.30 m, we can calculate the pressure at the bottom of the tank:
P = ρgh
= (789 kg/m³) * (9.8 m/s²) * (0.30 m)
= 2,307.54 Pa
Therefore, the pressure at the bottom of the tank is approximately 2,307.54 Pa.
To find the pressure at the bottom of the tank, we'll use the concept of hydrostatic pressure. The hydrostatic pressure at any point in a fluid is given by the equation:
P = ρgh
Where:
P = pressure
ρ = density of the fluid
g = acceleration due to gravity
h = depth of the fluid
First, let's determine the density of ethyl alcohol. The density of ethyl alcohol varies slightly with temperature, but at room temperature, it is approximately 789 kg/m³.
Next, we'll calculate the height (h) of the fluid in the tank. Since the tank is filled to a full depth of 0.30 m, the height of the fluid is also 0.30 m.
Now, we'll substitute the values into the equation:
P = (ρ)(g)(h)
P = (789 kg/m³)(9.8 m/s²)(0.30 m)
Calculating this expression will give us the pressure at the bottom of the tank.