Question

In: Physics

A spherical raindrop falling through fog or mist accumulates mass due to condensation at a rate...

A spherical raindrop falling through fog or mist accumulates mass due to condensation at a rate proportional to its cross-sectional area multiplied by the velocity.
a. Calculate the acceleration of the raindrop in terms of its radius and velocity. The raindrop starts from rest and has almost zero size.
b. If a terminal velocity of 10 m/s is reached at a raindrop radius of 1 mm, find the proportionality constant for the increase in the raindrop's mass with velocity.
c. find the relationship between the raindrop radius, r, and the height dropped, y. [Hint: v = dy/dt]
d. How far does the raindrop fall as it grows to a size of 1 mm?

Solutions

Expert Solution


Related Solutions

A spherical raindrop falling through mist builds up mass. The mass accumlates at a rate proportional...
A spherical raindrop falling through mist builds up mass. The mass accumlates at a rate proportional to its cross-sectional area and invers;ey proportional to its velocity, that is, dm/dt=k?r2/v, where r is the radius of the raindrop at a given time and v is the downard speed at the same time.Assuming the density P of the rain drop is a constant. Ignoring the resistance do to the fog and the air, calculate the instaneous acceleration of the raindrop as a...
Falling Drop A raindrop of mass mo, starting from rest, falls under the influence of...
4. Falling Drop A raindrop of mass \(m_{0}\), starting from rest, falls under the influence of gravity. Assume that as the raindrop travels through the clouds, it gains mass at a rate proportional to the momentum of the raindrop, \(\frac{d m_{r}}{d t}=k m_{r} v_{r}\), where \(m_{r}\) is the instantaneous mass of the raindrop, \(v_{r}\) is the instantaneous velocity of the raindrop, and \(k\) is a constant with unit \(\left[m^{-1}\right] .\) You may neglect air resistance.(a) Derive a differential equation for the...
A spherical raindrop 2.1 mm in diameter falls through a vertical distance of 3650 m. Take...
A spherical raindrop 2.1 mm in diameter falls through a vertical distance of 3650 m. Take the cross-sectional area of a raindrop = πr2, drag coefficient = 0.45, density of water to be 1000 kg/m3, and density of air to be 1.2 kg/m3. (a) Calculate the speed a spherical raindrop would achieve falling from 3650 m in the absence of air drag. (b) What would its speed be at the end of 3650 m when there is air drag? (Note...
A spherical raindrop 2.7 mm in diameter falls through a vertical distance of 5000 m. Take...
A spherical raindrop 2.7 mm in diameter falls through a vertical distance of 5000 m. Take the cross-sectional area of a raindrop = πr2, drag coefficient = 0.45, density of water to be 1000 kg/m3,and density of air to be 1.2 kg/m3. (a) Calculate the speed a spherical raindrop would achieve falling from 5000 m in the absence of air drag. 313.04 m/s (correct) (b) What would its speed be at the end of 5000 m when there is air...
A spherical raindrop 1.9 mm in diameter falls through a vertical distance of 5000 m. Take...
A spherical raindrop 1.9 mm in diameter falls through a vertical distance of 5000 m. Take the cross-sectional area of a raindrop = ?r2, drag coefficient = 0.45, density of water to be 1000 kg/m3, and density of air to be 1.2 kg/m3. Calculate the speed a spherical raindrop would achieve falling from 5000 m in the absence of air drag. What would its speed be at the end of 5000 m when there is air drag?
The mass flow rate of steam through an ideal Rankine turbine ( with an isentropic turbine...
The mass flow rate of steam through an ideal Rankine turbine ( with an isentropic turbine and an isentropic pump) is 30lbm/s. The water and or steam is at a pressure of 1000 psia throughout the boiler and superheater and exits the superheater at a temperature of 600 F. The condenser is at a pressure of 2 psia, and the water exits the condenser as a saturated liquid. Calculate the following. (a) the power output of the turbine (b) the...
Determine the mass flow rate of the refrigerant flowing through the condensor of a two-stage compression...
Determine the mass flow rate of the refrigerant flowing through the condensor of a two-stage compression refrigeration cycle (in kg/s). The fraction of the refrigerant that evaporates as it is throttled to the flash chamber is 0.19. The enthalpy of the refrigerant entering the evaporator is 55.14 kJ/kg and the enthalpy of the refrigerant leaving the evaporator is 239.19 kJ/kg. The amount of heat removed from the refrigerated space is 28 kW. (Round your answer to three decimal places).
A Rankine cycle uses water as its working fluid. The mass flow rate of water through...
A Rankine cycle uses water as its working fluid. The mass flow rate of water through the cycle is 150 kg/s. Superheated vapour exits the boiler at 8 MPa and 560 °C. The condenser pressure is 8 kPa. The water at the pump inlet is 35 °C. The isentropic efficiency of the pump is 75% and the isentropic efficiency of the turbine is 91%. The turbine and pump can be treated as adiabatic. The pressure drops of the working fluid...
Nitrogen (N2) goes through a constant area pipe (see figure below) at a mass rate of...
Nitrogen (N2) goes through a constant area pipe (see figure below) at a mass rate of 2 kg/s. It enters the pipe with a velocity of 17 m/s, a pressure of 500 kPa and a temperature of 177 C. It leaves the pipe at the same pressure (500 kPa) and a temperature of 67 C. The molar mass of N2 is 28 kg/kmol. Determine: a) The cross sectional area of the pipe in m2 . b) The velocity at the...
Nitrogen (N2) goes through a constant area pipe (see figure below) at a mass rate of...
Nitrogen (N2) goes through a constant area pipe (see figure below) at a mass rate of 2 kg/s. It enters the pipe with a velocity of 17 m/s, a pressure of 500 kPa and a temperature of 177 C. It leaves the pipe at the same pressure (500 kPa) and a temperature of 67 C. The molar mass of N2 is 28 kg/kmol. Determine: a) The cross sectional area of the pipe in m2 . b) The velocity at the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT