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.

Suppose a volcanic eruption at the bed of the ocean creates a new deepest point with a depth of 12.5 km below the surface of the ocean. Determine the pressure at this deepest point. Take the density of ocean water, ρ = 1030 kg/m³.

A uniform cylindrical glass barrel of radius 0.20 m is used to store wine. If the wine has a depth of 0.50 m and the pressure at the deepest point is 1.06 × 10⁵ Pa, determine the mass of the wine stored in the barrel.

A rectangular water tank has a length of X, a width of Y, and a height of Z. The tank is filled with salty water of density ρ. Determine an expression for the force experienced by a vertical face measuring Y by Z.

The vessel below is filled with fresh water (density = 1000 kg/m³). One of its arms is open to the atmosphere. Calculate the pressure at point N.

A tube filled with seawater (density = 1030 kg/m³) is shown below. One end is open to the atmosphere. What is the difference in pressure between i) points a and b? ii) points b and c?

A U-shaped tube has two equal water columns, 30 cm high on each side. Cooking oil (density = 920 kg/m³) is added to one side of the U-tube, creating a 30 cm oil column. The two liquids form separate layers. Determine the height difference of the top surfaces of liquids (water and oil) in the U-tube.

If a duct is at interstellar pressure (P = 4.0 × 10^-22 atm), find the circumference of a piston connected that suspends a 20 kg TV set in the air on the Earth's surface.  

If a 2.0 m long tube has one of its ends closed and the other end fitted with a thin, frictionless, and massless piston to trap air in the tube (Assume the 2.0 m length is initially filled with air at atmospheric pressure). Different liquids are poured on top of the piston to compress the trapped air. If the liquid used is freshwater, determine the length of the freshwater column that causes the greatest compression. Hint: Boyle's law states that p₁V₁ = p₂V₂ when a fixed amount of gas is compressed at a constant temperature, (assume constant gas temperature during compression). 

It can be shown using the ideal gas law that the density of a gas compressed by gravity changes exponentially following ρ = ρ₀e^-(y/y₀). y is the displacement from sea level (upward is positive), ρ₀ = 1.28 kg/m³ is the density of air at sea level, and y₀ is the scale height of the atmosphere. i) Use the weight of an air column to determine the value of y₀. ii) A commercial airline is cruising at 11500 m above sea level. Express air density at the cruising altitude as a percentage of air density at sea level. 

The expression P = F/A means that we can formulate an indirect way of measuring pressure in a vehicle's tires. A truck owner's manual states that a truck has a mass of 4300 kg and a transporter has placed a 3800 kg load on the truck. The loaded truck has 6 tires that bear 1/6 of the truck's mass and have equal air pressure. A weighbridge measures the flattened section of a tire that is in contact with the ground to be 27.9 cm by 9.2 cm. Determine the pressure of air in the tires.

During a tornado, strong winds of 200 km/h lifts off the roof of a car. If the value of the air density is 1.29 kg/m³ and if it is assumed that the car roof is measured to be 7.2 m × 11.4 m in size and is not bolted down, estimate what the weight of the car roof is that is blown away during the tornado.

Please use Bernoulli's principle to calculate what the lift force will be, in units of N, on a sail that has an area of 65 m², if the wind speeds over the front and back surfaces of the sail are 220 m/s and 130 m/s, respectively. Note that the density of air at sea level is 1.225 kg/m³.

Each breath expels approximately 80 cm3 of air at an average pressure of 106 mm-Hg. Using an assumption of 80 breaths per minute, find the lung's power output in watts.

A wire made of brass is used in a crane that can lift a maximum load of 6.0 × 10³ kg and has a safety factor of 9.0. Given that the maximum acceleration of the crane is 1.5 m/s² and the ultimate strength of brass is 2.5 × 10⁸ N/m², calculate the diameter of the wire.

A woodworker is planning on using an aluminum rivet to join two wooden planks together. The rivet should be able to handle shear forces up to about 2500 N. Given that the safety factor is 5, what should be the minimum diameter of the rivet that the woodworker must choose to use?

A submarine made mostly of steel is moving at a depth of 1500 m in the sea. At this depth, the pressure is 150 times that of the atmospheric pressure. Given that 1 atm = 1.0 x 10⁵ N/m² and the bulk modulus is 140 x 10⁹ N/m², calculate by what percentage the interior volume of the submarine would change descending from the surface of the sea.

What is the maximum force that a steel guitar string with a diameter of 0.97 mm can withstand before breaking? [Hint: The ultimate tensile strength of the steel is about 5.0 × 10⁸ N/m²]

A bass string made of steel with a diameter of 1.2 mm can withstand a maximum force of 570 N before breaking. Would using thinner or thicker strings help prevent snapping under high tension, and why does it snap when plucked? [Hint: The ultimate tensile strength of the steel is about 5.0 × 10⁸ N/m²]

A 1.4 m high container is full of oil. Determine the pressure difference in mm-Hg between the top and bottom of the container given that the density of the oil is 7.5 × 10² kg/m³ and 1.0 mm-Hg = 130 N/m².

A deep-sea diver measures the absolute pressure at his current depth to be 320 atmospheres. If the surface area of his helmet's viewing port is 8.0 × 10^-3 m², calculate the magnitude of the force exerted by water on it.

An aquarium has a vertical rectangular viewing window with a height $h$ and a width $w$. The aquarium is filled with water up to a height h. Assuming the density of water is $ρ$, use integration to determine the total force of the water on the window.

In the figure given below a uniform horizontal steel H-beam (of mass M = 1500 kg) rests on two columns of aluminum. What should be the minimum cross-sectional area of the two columns to support the beam if a safety factor of 8.0 is required? Assume that the ultimate strength for tension and compression for aluminum are both 2.0 × 10⁸ N/m².

An oil barometer is used in an experiment to measure atmospheric pressure. Given that the density of the oil used is $8.50\times 10^2\ \frac{kg}{m^3}$, calculate the height the oil column reaches under standard atmospheric conditions. Hint: Standard atmospheric pressure = 1.01 × 10⁵ Pa.

A rectangular tank filled with oil is accelerating uniformly from rest along a straight path on a flat surface, with an acceleration $a$ to the left. The surface of the oil forms an angle $\phi =\tan ^{-1}\left(\frac{a}{g}\right)$ with the horizontal. Determine the variation in pressure with depth below the oil surface.

In a hospital, an intravenous transfusion setup involves a bottle containing a saline solution with a density of 1.00 g/cm³. To achieve a liquid pressure of 55.0 mm-Hg at the patient's arm, how high must the bottle be positioned above the insertion site?

An intravenous drip contains a medication with a density of 0.98 g/cm³. If the patient's blood pressure measures 65 mm-Hg, determine the necessary height to hang the medication bottle so that it flows into the vein naturally under gravity.

A swimming pool float is being inflated using a foot pump. The initial pressure inside the float is 120 kPa (17.4 psi), and the final pressure is 220 kPa (31.9 psi). If the diameter of the foot pump plunger is 4.00 cm, determine the range of force applied to the pump handle throughout the inflation process.

Using the known value of atmospheric pressure of 610 N/m² on Mars's surface, calculate the estimated total mass of Mars's atmosphere. The radius of Mars is 3.4 × 10⁶ m and the gravitational acceleration on Mars's surface is 3.7 m/s².

A mountain climber quickly descends vertically at an average speed of about 8.0 m/s due to bad weather conditions and starts experiencing ear discomfort due to rapid changes in air pressures around him/her. What could be his/her tolerance limit for the increase in air pressure (dP/dT)?

A scuba diver descends to a depth of 5.0 × 10² m underwater. If the area of his eardrum is 0.25 cm², what would be the force on his eardrum due to this change in depth if the pressure in his ears is not equalized to that of the water?

A steel column with a cross-sectional area of 1.5 m² supports a mass of 25,000 kg. Given that the column is 7.5 m in height, calculate the amount of compression. Use a Young's modulus of 200 GPa for steel.

A person of mass 85 kg accidentally falls off a helicopter into a haystack. The area of impact was later found to be 0.25 m² and the velocity with which the person landed was 45 m/s. If he was stopped after traveling a distance of 1.5 m into the hay and the ultimate strength of body tissue is 4.6 x 10⁵ N/m², evaluate if he can escape significant injuries.

In the figure below, two trucks are pulling the ends of a steel cable (of diameter 1.5 mm) that goes over two pulleys attached at the top of the two 4.0 m high columns. This raises the 35 kg anvil attached to the cable in the middle. If the columns are 6.5 m apart and the trucks pull the cable in a way that the anvil only has vertical motion, determine the height of the anvil at which the cable breaks. [Hint: Assume that the ultimate tensile strength of steel is 5.0 × 10⁸ N/m².]

An athlete of 85 kg falls off from a height of 5.0 m to the floor. However, he gains balance and lands on stiff legs. As a result, his center of gravity moves down by a distance of D = 1.2 cm after his feet touch the ground. Determine the stress and conclude if his fibula would break because of it. Assume that the cross-sectional area of the fibula at the middle is 1.4 × 10^-4 m², and the ultimate strength of the bone is 1.30 × 10⁸ N/m².