A column of water has a diameter of 2 m and a depth of 8.6 m. How much pressure is at the bottom of the column? The acceleration of gravity is 9.8 N/kg.
Answer in units of Pa
Ignore diameter. It's irrelevant and tries to make it a trick question. And N/kg = m/s/s.
Just do the pressure in fluids equation, P = ρhg. And water also has a density of 1000 kg/m^3.
So all you have to do is:
P = (1000 kg/m^3)(8.6 m)(9.8 m/s/s)
So your answer is 84,280.
Well, well, well, let's dive into this question, shall we? The pressure at the bottom of the column is equal to the weight of the water above it divided by the area of the bottom of the column. Let's do some math here. The weight of the water is equal to the density of water times the volume of water. Since the density of water is about 1000 kg/m³ and the volume of water is the cross-sectional area times the height, we can calculate the weight of the water. Now, the cross-sectional area is equal to πr², where r is the radius. Since you gave me the diameter, you'll need to do a little math to find the radius. Once you have the radius, you can plug it into the formula and calculate the pressure. Don't forget to convert the depth into meters! And voila, you'll get your answer in units of Pa. Good luck!
To calculate the pressure at the bottom of the water column, we can use the equation:
Pressure = Density * Gravity * Height
First, let's calculate the density of water. The density of water is approximately 1000 kg/m³.
Next, we can calculate the height of the water column. The diameter of the water column is given as 2 m, so the radius is half of that, which is 1 m. The depth of the column is given as 8.6 m.
The height of the water column is the height of the cylindrical column, which is equal to the depth of the column, so the height is 8.6 m.
Now we can substitute the values into the formula:
Pressure = (1000 kg/m³) * (9.8 N/kg) * (8.6 m)
Calculating this gives us:
Pressure = 84,280 Pa
Therefore, the pressure at the bottom of the water column is 84,280 Pa.
To calculate the pressure at the bottom of the column, we can use the formula:
Pressure = density × acceleration due to gravity × height
First, we need to calculate the density of water. The density of water is approximately 1000 kg/m³.
Now, let's break down the steps to find the pressure:
Step 1: Calculate the cross-sectional area of the column.
The diameter of the column is given as 2 m. We can use this to find the radius: radius = diameter/2.
Plugging in the values: radius = 2 m/2 = 1 m.
Now, we can calculate the cross-sectional area of the column using the formula: Area = π × radius².
Step 2: Calculate the pressure.
Using the values we obtained, we can calculate the pressure:
Pressure = density × acceleration due to gravity × height.
Plugging in the known values: Pressure = 1000 kg/m³ × 9.8 N/kg × 8.6 m.
Now, let's calculate the pressure:
Area = π × (1 m)² = π m² (approximately 3.1416 m²)
Pressure = 1000 kg/m³ × 9.8 N/kg × 8.6 m
Pressure = 84328 Pa (approximately)
Therefore, the pressure at the bottom of the column is approximately 84328 Pa.