(a) Let s(t) be the amount of salt in the tank at time t. Find a differential equation governing s(t).

Please help. This problem involves finding the radius and volume of a platinum atom using its density. Thank you.

The Ekman number, Ek, arises in geophysical fluid dynamics. It is dimensionless parameter combining seawater density ρ, a characteristic length L, Seawater viscosity μ, and the Coriolis frequency Ωsinφ, where Ω is the rotation rate of the earth and φ is the latitude angle. Determine the correct form of Ek if the viscosity is in the numerator.

The density of platinum is 21500 kg/m3 and that of aluminum is 2702 kg/m3. Find the ratio of the volume of 1.20 kg of platinum to the volume of 1.01 kg of aluminum.

In 1923, the United States Army (there was no United States Air Force at that time) set a record for in-flight refueling of airplanes. Using two refueling planes, an Airco DH-4B biplane was able to remain in flight for 35 h. During the flight, the refueling planes were able to air-transfer a total of 687 gallons of fuel to the plane in 9 refueling transfers. Assume that the refueling nozzle had a diameter of 1.65 in and each refueling took 2.43 min to perform. Calculate the velocity of the fuel through the nozzle. Assume that the fuel filled the entire cross-sectional area of the nozzle. velocity: 12.94 m/s Incorrect

A smoking room is to accommodate 50 smokers. The fresh air requirement for smoking areas is specified to be 40 L/s per person. The air velocity in the ventilation duct is 8 m/s. Determine: b) The diameter of the ventilation duct in [cm] SOLUTION

Consider a water tank that is being filled with rainfall at the top and is drained through a small hole atthe bottom. The change in volume can be modelled by considering the amount of water entering andleaving the tank (per unit of time) as followsdVdt= fin − fout.Here volume of water in the tank V is in litres, flow rate in fin is in litres per hour, flow rate out fout isin litres per hour and time t is in hours. Initially, the tank contains 50L of water: V (0) = 50.(a) Assume the rainfall throughout the day is getting heavier, such that, fin(t) = 10 + t andthat the tank is losing 10% of its volume of water per hour, such that, fout(V ) = 0.1V . Check bydirect substitution that the functionV (t) = 10(t + 5e−0.1t)satisfies the ODE and the initial condition.Now assume that the hole is slowly growing in size, so that the flow rate out increaseswith time:fout(V, t) = 0.1(1 + 0.1t)V.Solve the ordinary differential equation for V (t) with this flow rate out, using either separation…