What is the area of the input piston if a hydraulic press is used to lift a heavy crate with a mass of 970 kg to a height of 40 cm, with an output piston diameter of 44 cm and an input force of 420 N?

An open tube manometer is used at a location where the atmospheric pressure is 0.783 atm. The fluid used in the tube has a density of 0.900 g/cm³, and the manometer column height is 30 cm, as shown in the image. Calculate i) the absolute pressure (p) within the gas tank, ii) the absolute pressure at the bottom (p_bot) of the manometer, iii) the absolute pressure 15 cm above the bottom (p₁₅), and iv) the gauge pressure (p_gauge) of the gas tank.

A hollow metallic container of mass 400 kg (with a square base) is floating in water. The length of the base is 1.0 m. A 70.0 kg person holding luggage of mass 20 kg jumps into the container. What extra height of the container will be submerged? 

A floating platform possesses a rectangular base with dimensions of 4 m by 8 m and a 1.5 cm thickness, made from a material with a density of 8100 kg/m³. The platform is enclosed by walls constructed from platinum, having a 0.32 cm thickness. Find the lowest height necessary for these walls to ensure the platform remains afloat in the lake. The density of water is approximately 1000 kg/m³.

In an underwater-themed restaurant, a large decorative aquarium displays a captivating liquid with a density ρ. This tank has the shape of a rectangular parallelepiped, with dimensions L (length), H (height), and W (width), as shown in the figure. A spring is used to prevent the front glass panel of the aquarium from being pushed out at the bottom by counteracting the torque on the panel. Determine the minimum height above the bottom at which the spring should be fixed, given that it has the minimum tension. Note: The tank has an opening to the atmosphere. 

Reducers are devices that connect pipes of different cross-sections. A pipeline has a reducer that connects a 3.0 inch diameter pipe to a 2.0 inch diameter pipe. If water in the large pipe flows at 10 cm/s, how quickly does water flow in the narrow pipe?

Capillary action causes water to rise in a tube due to adhesive forces between water and the walls of the tube. Suppose a capillary action pump moves water through a compound pipe with a net flow rate of 50 g/h. If the compound pipe has 3500 bores each of diameter 600 μm, find the water speed (in mm/s) in the bores. Assume the water is salty with a density of 1010 kg/m³.