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In each of these problems, begin by deriving the governing equation using energy balances (even if we already derived the governing equation in class). This is important to practice.
1) Consider one-dimensional, steady state conduction through the wall of a pipe. The pipe has inner diameter Di and outer diameter Do. If the outside of the pipe is fixed at temperature To, and inside the pipe there is a convective boundary condition with T = T∞ and convective heat transfer coefficient h, find the temperature profile in the pipe.
2) Solve for the temperature profile in an extended fin of length L, with the prescribed temperature boundary condition, that is, T(L) = TL. What is the fin efficiency for this fin?
3) Consider one-dimensional transient conduction in a slab of thickness L. Initially, the entire slab is at temperature Ti and both surfaces are at temperature Ti. At time t = 0, the left surface (x = 0) temperature is increased to Ts. Find the temperature profile in the slab as a function of time. (Note the solution to this problem involves eigenfunctions).
Raw primary sludge at a solids concentraion of 4% is mixed with waste activated sludge at a solids concentration of .5%. The flows are 20 and 24 gal/min respectively.
On average, is an electron farther away from the nucleus when it isoccupying a 2p orbital in hydrogen than when it is occupying a 2sorbital? Justify by calculating the average distances
A force, 90 N in magnitude, is applied to control rod AB as shown. Knowing that the length of the rod is 225 mm, determine the moment of the force about point B by resolving the force into components along AB and in a direction perpendicular to AB..
Calculate the pressure p and the force T per linear mm along the (imaginary) longitudinal seam in the pipe at a point that is 100 metres below the open (free) water surface of the reservoir.
A paper plant is proposed for a location 1 km upwind from a town. It will emit 40 g/s of hydrogen sulfide, which has an odor threshold of about 0.1 mg/m 3. Winds at the effective stack are typically 4 m/s blowing toward the town.
Exhaust gas from a chemical process flows at a rate of 8,000 actual cubic feet per minute (acfm) from point A at 250°F and 1 atm pressure. It flows through a circular duct to a fan
A barge measures 10 ft (depth) by 35 ft by 120 ft and weighs 100 U.S. tons. The barge floats in fresh water (specific weight = 62.4 lb/ft3) and is evenly filled with 38,000 bushels of corn (60 lb/bushel).
It is proposed to estimate the seepage flow rate through the foundation soil using the flow net sketching technique. For this purpose, calculate the horizontal scale factor and effective hydraulic conductivity of the foundation soil.
The heated water outflow from a nuclear power plant is cooled in a 50-m wide rectangular channel that has a discharge Q = 225.0 m^3/s. The Manning's n is 0.015 and the bed slope is 5.0 X 10^-4
If water vapor in the atmosphere has a partial pressure of 3500 Pa and the temperature is 30 degrees Celsius, what is its specific weight?
A freeway has a capacity of 4500 veh/hr. A traffic accident occurs at 9AM and the freeway is closed. At 9:15 AM, the freeway is partially opened with capacity of 1500 veh/hr. Freeway is restored to full capacity 4500 veh/hr at 9:30 am.
Calculate the pressure inside a 2-mm diameter bubble of water at 20°C and compare with the pressure inside a 2-mm diameter droplet of water at 20°C.
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