This problem asks to set up an integral to calculate the amount of work to empty the tank through the spout at the top. The tank is 8 ft in height filled to 5 ft with water. It has a smaller diameter of 4 ft and larger diameter of 6 ft. The spout on top is 1 ft above the tank. Weight is given as 62.5 lbs/ft3 and density of water (volume) as 1000 kg/m3. Gravity/Acceleration is 9.8 m/s2 I've only done problems with cylindrical tanks but this one is shaped differently so I'm thinking it will change how to do the problem when drawing the cross section inside the tank. If I could get a step by step of all the work used to set up a final integral for the total amount of work to empty the tank that'd be great. The steps I'm looking for (if possible) include going from finding: As to Vs to Ms to Fs to Ws to finally Work Total (Wt) These being area, volume, mass, force, work and "s" subscribt representing "slice" I've attached a picture of the tank with measurements The integral doesn't need to be solved just set up as Work Total (Wt)
This problem asks to set up an integral to calculate the amount of work to empty the tank through the spout at the top.
The tank is 8 ft in height filled to 5 ft with water. It has a smaller diameter of 4 ft and larger diameter of 6 ft. The spout on top is 1 ft above the tank. Weight is given as 62.5 lbs/ft3 and density of water (volume) as 1000 kg/m3. Gravity/Acceleration is 9.8 m/s2
I've only done problems with cylindrical tanks but this one is shaped differently so I'm thinking it will change how to do the problem when drawing the cross section inside the tank. If I could get a step by step of all the work used to set up a final integral for the total amount of work to empty the tank that'd be great.
The steps I'm looking for (if possible) include going from finding:
As to Vs to Ms to Fs to Ws to finally Work Total (Wt)
These being area, volume, mass, force, work and "s" subscribt representing "slice"
I've attached a picture of the tank with measurements
The integral doesn't need to be solved just set up as Work Total (Wt)
Step by step
Solved in 5 steps with 1 images
