Intro to Pressure Practice Problems

A deep sea water vessel operates at 2.9 km below the surface of seawater. Determine the pressure a gauge would record at the operating depth. Assume the density of water remains constant as depth increases.

A person breathes with aid of the pressure difference between the lungs and the atmosphere. A lifesaver on a rescue mission underwater decides to use a snorkel tube that links lungs to the atmosphere at the surface of the water. The increasing water depth collapses the chest cavity, and consequently, decreases the pressure difference experienced in the lungs. Determine the pressure difference between the inside and the outside of the lungs when the lifesaver is 5.0 m below the surface of the water. Inside pressure is equal to atmospheric pressure.

Jupiter is the largest known planet in the solar system. Its atmospheric pressure is 9.87 atm and gravitational acceleration is 2.63g. A sealed circular container containing soda (mainly water) and compressed air at a pressure of 9.87 atm above the soda is taken to Jupiter for an experimental study. The soda column is 25.40 m high and the container has a diameter of 1.60 m. Determine the force experienced at the bottom of the container due to Jupiter's atmosphere. Ignore the effects of temperature.

A long experimental container is placed with its length vertical. The container is filled with seawater. In one instance, the air above the water column has a pressure equal to atmospheric pressure while a pressure gauge connected to the lowest point of the water column reads 11760 Pa. The container is connected to a pressurized air supply, adding air and raising the pressure above the water column by 2500 Pa. Determine the reading on a pressure gauge connected to the lowest point of the water column. (1 atm = 1.01 × 10⁵ Pa)

A drum with a 0.800 m high layer of oil is left outside for some time. The drum collects rainwater, creating a 0.400 m thick layer of water. The oil has a density of 750 kg/m3. i) Calculate the gauge pressure at the boundary of the two layers. ii) Calculate the gauge pressure at the bottom of the drum.

A pressure sensor has a higher limit of 2.5 N above the force it experiences at atmospheric pressure. It is used to measure pressure at various depths in the ocean. Determine the greatest depth that the sensor can go without damaging it. The diameter of the sensor is 6.4 mm.

Siphoning fluids with a pipe is a common practice, despite the risk of choking. The water level in a tall tank is fairly low. A pipe is inserted into the water in the tank. A person sucks on the other end of the pipe lifting water by 1.0 m above the level of water in the tank but doesn't succeed in making water flow through the siphon. i) Determine the least gauge pressure attained inside the person's lungs during this activity. ii) Why is the pressure negative?

A newly discovered planet has a 1.2 km deep ocean. The gravitational acceleration on that planet is 5.20 m/s². i) Assuming the ocean is filled with fresh water, determine the gauge pressure at the bottom of the ocean. ii) Determine the depth of the earth's ocean where a gauge would record similar pressure.

A submarine operates at a depth of 450 m below the surface of seawater. The submarine has a square glass window of length 20 cm. Determine the net force on the window from the ocean water and air inside the submarine. Assume air pressure inside the submarine is equal to the pressure at the surface of the ocean; pressure remains constant on the entire window surface; the density of water remains constant as depth increases. 

A waterline engineer wishes to add a fertilizer solution to a pipeline in a practice called fertigation. The gauge pressure of water flowing in a pipe is 17.5 kPa. The fertilizer solution of density 1020 kg/m³ is placed inside a tank. Determine the least height of the tank above the pipeline that drives the fertilizer solution through a connecting hose into the pipe.  

Most bike frames are made of either carbon fiber or aluminum, and tests are conducted to determine the structural performance properties of these materials. Identical bars of carbon and aluminum, each of length 0.5 m and radius 5 mm, are subjected to a 2000 N tensile force. The Young's modules for carbon and aluminum are 1.81 × 10¹¹ Pa and 6.9 × 10¹⁰ Pa, respectively. Calculate i) the strain (S) and ii) the elongation (Δl) of each bar.