# Homework Help: Cloud movement, finding temperature, velocity and height from this formula

1. Oct 10, 2011

### automan13

1. An unsaturated parcel of air is entrained into a cloud near the region of the cloud top. the updraft velocity U, the ambient lapse rate in ther cloud γ, the entrainment rate E, and the mixing ratio of the condensed water μcan be considered constants along the trajectory of the parcel.
assuming that at t=0 the velocity of the parcel is Up and its acceleration is zero.
Obtain from equations, analytical solutions for the evolution in time of the parcel's velocity, temperature and height.
for simplicity, assume that the term g(Tp-T)/T can be approximated by g(Tp-T)/To where To is a constant average temperature in the cloud. Show that for To=-15℃ and γ=6℃/km, this time equals approximately 4.3 minutes.

2. d/dt(Tp - T) = -E (Lm/Cp)- (P - λc) dz/dt
dUp/dt=(Tp-T)/T g + gm - E (Up - U)

Tp= temperature
Up= velocity
z=height

3. Really bad at math and physics, ANY help at understanding the equations and the problem is really appreciated. Thanks in advance.