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Chapter 3: Problem 48

The viewing window in a diving suit has an area of roughly \(65 \mathrm{cm}^{2}\). (a) If an attempt were made to maintain the pressure on the inside of the suit at 1 atm, what force (N and Ibt) would the window have to withstand if the diver descended to a depth of 150 m. Take the specific gravity of the water to be 1.05. (b) Repeat the calculation of Part (a) for the deepest Guiness-verified SCUBA dive.

Short Answer

Expert verified
The force the window would have to withstand at a depth of 150m can be calculated by first calculating the pressure at that depth, and then the force exerted on the window by that pressure. The same process can be used to calculate the force for the deepest Guinness-verified scuba dive, using the record depth instead of 150m.

Step by step solution

01

Determining the pressure at a particular depth

The pressure \( P \) at a particular depth \( d \) underwater is given by the equation: \( P = P_0 + \rho gh \), where \( P_0 \) is the atmospheric pressure (1 atm), \( \rho \) is the specific gravity of the water, \( g \) is acceleration due to gravity (9.81 m/s虏), and \( h \) is the depth. In the first case, this is 150 m, and the specific gravity of the water is given as 1.05. Substitute these values into the equation to find the pressure.
02

Calculating the force exerted on the viewing window

The force \( F \) exerted on the viewing window by this pressure can be calculated from the equation: \( F = P \times A \), where \( A \) is the area of the viewing window. In this case, 65 cm虏. Convert this area to m虏 (since the pressure is in Pascals, which is N/m虏), and then substitute the calculated pressure and the area into the equation to find the force.
03

Repeat the process for the deepest Guiness-verified SCUBA dive

The process for part (b) is the same as for part (a), only you will need to check the official Guinness World Records for the depth of the deepest verified scuba dive. Use this new depth instead of 150m and follow the same steps to calculate the force the window would need to withstand at that depth.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Buoyancy
Buoyancy is the upward force that keeps objects afloat in a fluid. This phenomenon occurs because the pressure at the bottom of an object submerged in a fluid is greater than the pressure at the top. This pressure difference results in a net upward force, which is what we call buoyancy.
For instance, when a diver descends underwater, they experience this buoyant force opposing their weight. Buoyancy can be calculated using Archimedes' principle, which states that the buoyant force on a submerged object is equal to the weight of the fluid that the object displaces.
Understanding buoyancy is crucial for divers. It helps them determine how their equipment will behave underwater. Additionally, it is a key factor in ensuring their safety and stability while diving.
Hydrostatic Pressure
Hydrostatic pressure is the pressure exerted by a fluid at equilibrium due to the force of gravity. This type of pressure increases with depth, as the weight of the fluid above adds to the pressure experienced at a given level.
For a diver, hydrostatic pressure is significant because it determines the force exerted on their body and equipment, including the viewing window of a diving suit. The equation used to calculate hydrostatic pressure is:
\[ P = P_0 + \rho gh \]
Here:
  • \( P_0 \) is the atmospheric pressure at the surface, typically 1 atm.
  • \( \rho \) is the density of the fluid, or specific gravity.
  • \( g \) is the acceleration due to gravity, approximately 9.81 m/s虏.
  • \( h \) is the depth of the fluid.
Bear in mind that as a diver descends, they must manage increased pressure to avoid physical harm. Understanding hydrostatic pressure aids in calculating the forces involved and planning safe diving practices.
Applied Force
Applied force refers to the force that needs to be exerted on an object to withstand external pressures or forces. In the context of diving suits, it involves understanding the force exerted on surfaces like the viewing window to avoid structural failure.
The equation to calculate the applied force on a surface due to pressure is:
\[ F = P \times A \]
Where:
  • \( F \) is the force applied.
  • \( P \) is the pressure exerted on the surface.
  • \( A \) is the area of the surface.
This formula shows that both the pressure on the surface and the area over which it acts are crucial in determining the force applied. For divers, the applied force is a key consideration as they descend to greater depths, where pressure increases significantly.
By understanding how to calculate and manage applied forces, divers and engineers can design safer equipment that withstands the challenging environment of underwater exploration.

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Most popular questions from this chapter

A rectangular block of solid carbon (graphite) floats at the interface of two immiscible liquids. The bottom liquid is a relatively heavy lubricating oil, and the top liquid is water. Of the total block volume, \(54.2 \%\) is immersed in the oil and the balance is in the water. In a separate experiment, an empty flask is weighed, \(35.3 \mathrm{cm}^{3}\) of the lubricating oil is poured into the flask, and the flask is reweighed. If the scale reading was \(124.8 \mathrm{g}\) in the first weighing, what would it be in the second weighing? (Suggestion: Recall Archimedes' principle, and do a force balance on the block.)

An open-end mercury manometer is connected to a low-pressure pipeline that supplies a gas to a laboratory. Because paint was spilled on the arm connected to the line during a laboratory renovation, it is impossible to see the level of the manometer fluid in this arm. During a period when the gas supply is connected to the line but there is no gas flow, a Bourdon gauge connected to the line downstream from the manometer gives a reading of 7.5 psig. The level of mercury in the open arm is \(900 \mathrm{mm}\) above the lowest part of the manometer. (a) When the gas is not flowing, the pressure is the same everywhere in the pipe. How high above the bottom of the manometer would the mercury be in the arm connected to the pipe? (b) When gas is flowing, the mercury level in the visible arm drops by \(25 \mathrm{mm}\). What is the gas pressure (psig) at this moment?

An inclined manometer is a useful device for measuring small pressure differences. The formula given in Section 3.4 for the pressure difference in terms of the liquid-level difference \(h\) remains valid, but while \(h\) would be small and difficult to read for a small pressure drop if the manometer were vertical, \(L\) can be made quite large for the same pressure drop by making the angle of the inclination, \(\theta,\) small. (a) Derive a formula for \(h\) in terms of \(L\) and \(\theta\) (b) Suppose the manometer fluid is water, the process fluid is a gas, the inclination of the manometer is \(\theta=15^{\circ},\) and a reading \(L=8.7 \mathrm{cm}\) is obtained. What is the pressure difference between points? and?? (c) The formula you derived in Part (a) would not work if the process fluid were a liquid instead of a gas. Give one definite reason and another possible reason.

As will be discussed in detail in Chapter \(5,\) the ideal-gas equation of state relates absolute pressure, \(P(\mathrm{atm}) ;\) gas volume, \(V(\text { liters }) ;\) number of moles of gas, \(n(\mathrm{mol}) ;\) and absolute temperature, \(T(\mathrm{K}):\) $$P V=0.08206 n T$$ (a) Convert the equation to one relating \(P(\mathrm{psig}), V\left(\mathrm{ft}^{3}\right), n(\mathrm{lb}-\mathrm{mole}),\) and \(T\left(^{\circ} \mathbf{F}\right)\). (b) \(\mathrm{A} 30.0\) mole \(\%\) CO and 70.0 mole \(\% \mathrm{N}_{2}\) gas mixture is stored in a cylinder with a volume of \(3.5 \mathrm{ft}^{3}\) at a temperature of \(85^{\circ} \mathrm{F}\). The reading on a Bourdon gauge attached to the cylinder is 500 psi. Calculate the total amount of gas (lb- mole) and the mass of \(\mathrm{CO}\left(\mathrm{Ib}_{\mathrm{m}}\right)\) in the tank. (c) Approximately to what temperature \(\left(^{\circ} \mathrm{F}\right)\) would the cylinder have to be heated to increase the gas pressure to 3000 psig, the rated safety limit of the cylinder? (The estimate would only be approximate because the ideal gas equation of state would not be accurate at pressures this high.)

since the 1960 s, the Free Expression Tunnel at North Carolina State University has been the University's way to combat graffiti on campus. The tunnel is painted almost daily by various student groups to advertise club meetings, praise athletic accomplishments, and declare undying love. You and your engineering classmates decide to decorate the tunnel with chemical process flowcharts and key equations found in your favorite text, so you purchase a can of spray paint. The label indicates that the can holds nine fluid ounces, which should cover an area of approximately \(25 \mathrm{ft}^{2}\). (a) You measure the tunnel and find that it is roughly 8 feet wide, 12 feet high, and 148 feet long. Based on the stated coverage, how many cans of spray paint would it take to apply one coat to the walls and ceiling of the tunnel? (b) Having just heard a lecture on process safety in your engineering class, you want to take appropriate safety precautions while painting the tunnel. One useful source for this type of information is the Safety Data Sheet (SDS), a document used in industry to provide workers and emergency personnel with procedures for safely handling or working with a specified chemical. Other sources of information about hazardous substances can be found in handbooks, and some countries, including the United States, have laws that require employers to provide their employees with Safety Data Sheets. \(^{6}\) Besides composition information, the SDS contains information such as physical properties (melting point, boiling point, flash point, etc.), other threats to health and safety, recommended protective equipment, and recommended procedures for storage, disposal, first aid, and spill handling. The SDS can typically be found online for most common substances. Search the web for "spray paint SDS" and find a representative SDS for a typical spray paint product. Based on the document you find, what are the top three hazards that you might encounter during your tunnel painting project? Suggest one safety precaution for each listed hazard.
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