Derive an expression for the variation of density with respect to height in the atmosphere with constant potential temperature. Please show the full derivation and label variables/constants(Atmospheric Dynamics)
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- please answer the following A large truck tire is inflated to a gauge pressure of 86 psi. The total area of one sidewall of the tire is 1,220 in2. What is the net outward force (in lb) on the sidewall because of the air pressure? (Enter the magnitude.)If sea level is 101350pa ,calculate the standard pressure at an altitude of 5000m using (a) the exact formula (b) an isothermal assumption at a standard sea level temperature of 15°C. Is the isothermal approximately adequate?Gauge pressure is the pressure read by a pressure gauge. The gauge pressure will be zero if the pressure is the same as the general atmospheric pressure, because the gauge measures only the excess above atmospheric pressure. The actual pressure will thus be atmospheric pressure plus gauge pressure. Atmospheric pressure is about 14 pounds per square inch. The Rankine temperature scale is the Fahrenheit verson of the absolute temperature, and absolute zero in Rankine is about -460 F. Now, imagine a football has been stored in a warm locker room at a temperature of 71 F, and has a gauge pressure of 12.5 pounds per square inch. Next, it is taken outside and cooled to 40 F. What will the gauge pressure be after this is done?
- In a hurricane, the mean sustained wind velocity v (in meters per second) can be modeled by v(p) = 6.31013-p, where p is the air pressure in millibars at the center of the hurricane. Estimate the air pressure, p, at the center of the hurrican when the mean sustained wind velocity, (v(p)), is 60 meters per second. Round to the nearest hundredth. mbar Blank 1:What are the air-standard assumptions?Devices like Fitbits determine whether you have climbed stairs by determining when the atmospheric pressure changes while you are walking. By what percentage should the atmospheric pressure change when you climb a flight of stairs? You may assume the atmosphere is entirely nitrogen and that the temperature is 25 degrees celsius, and that the flight of stairs is 10 feet elevation change in total.
- A submarine dives down to a depth 80 metres beneath the surface of the ocean. Calculate the pressure in atmospheres at that depth, assuming the density of water is 1029 kg/m3, and the air pressure at the surface is 105.2 kPa. Give your answer with two digits of precision. Note: 1 standard atmosphere is 101325 Pa. Your Answer: AnswerAssume that a raindrop has a volume of 0.05 cm^3 and you need an Avogadro's number of raindrops to fill up the cubic water tank. What is the length of the edge of the tank?