The Trent-Severn Waterway Lift Lock 21, better known as the Peterborough lift lock, was constructed with two caissons (water-tight compartments) atop two large pistons (each with a diameter of 2 m) in the early 20th century. Each caisson is 42.4 m long and 9.7 m wide and fills with water to a depth of 2.1 m. To raise and lower the caissons, the lock operators allow a little more water into the top caisson, making it slightly heavier than the bottom caisson, and a valve is opened between the hydraulic cylinders, allowing hydraulic fluid to move between them.

The heavier caisson drops to the bottom position and pushes the lighter caisson to the top position. Each piston travels 19.8 m during this process, which takes about 165 seconds. Next, the valve is closed to lock the caissons in place and the gates are opened to allow the boats in each caisson to access the next stage in the waterway, and to allow waiting boats to enter for the next lock cycle.

QUESTIONS:

1. What is the volume of water in one caisson?
2. What is the mass of water in one caisson?
3. What is the force pushing down on each piston? Ignore the weight of the structure; assume that the force pushing down on each piston is the weight of the water in the caisson.
4. What is the pressure of the hydraulic fluid in this system?
5. What is the volume of hydraulic fluid that moves between the cylinders during one cycle of the lock's operation?
6. What is the volumetric flow rate of hydraulic fluid between the cylinders while the caissons are in motion?