The pressure at the bottom of a cylindrical container with a cross-sectional area of 46.5 cm2 and holding a fluid of density 480 kg/m3 is 115 kPa.
(a) Determine the depth of the fluid.
(b) Determine the pressure at the bottom of the container if an additional 3.00 10-3 m3 of this fluid is added to the container. (Give your answer to at least 3 significant figures.)
To solve this problem, we can use the concept of pressure in a fluid, which is given by the formula:
Pressure = Density x Acceleration due to gravity x Height
(a) To determine the depth of the fluid, we can rearrange the formula to solve for height:
Height = Pressure / (Density x Acceleration due to gravity)
Given:
Pressure = 115 kPa = 115,000 Pa
Density = 480 kg/m3
Acceleration due to gravity = 9.8 m/s2
Substituting these values into the formula, we get:
Height = 115,000 Pa / (480 kg/m3 x 9.8 m/s2)
First, we need to convert the cross-sectional area of the container from cm2 to m2:
Area = 46.5 cm2 = 46.5 x 10-4 m2
Now, we can calculate the height:
Height = 115,000 Pa / (480 kg/m3 x 9.8 m/s2 x 46.5 x 10-4 m2)
Using a calculator, we can solve this equation to find the height of the fluid.
(b) To determine the pressure at the bottom of the container after adding additional fluid, we need to consider the new volume of the fluid and calculate the new pressure.
Given:
Additional volume of fluid = 3.00 x 10-3 m3
The new total volume of the fluid in the container would be the initial volume plus the additional volume. So, the total volume is:
Total Volume = Initial Volume + Additional Volume
We can calculate the initial volume using the formula:
Initial Volume = Area x Height
After finding the initial volume, we can calculate the total volume and then determine the new height using the formula for the initial height. Finally, we can calculate the new pressure at the bottom of the container using the formula mentioned earlier, with the new height and the given density.
Using these methods, we can solve parts (a) and (b) of the problem.