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Problem 5.13
Rain on roof
A violent rainstorm hits a roof inclined at an angle
θ
from the horizontal. The rain pours
down at a mass flow rate ˙
m
per unit horizontal area, each drop falling vertically at a
speed V. Soon a steady state is established where the water (density
ρ
) flows down the
roof while the raindrops splatter violently into the layer from above and mix into it. We
are interested in estimating the water layer thickness distribution h(x) on the roof.
The roof inclination angle
is not small (think of order 45 degrees). The slope of
the water surface relative to the roof is small, however (
dh/dx
<<1); the water flow is
almost (but not quite) parallel to the roof. The principal driving forces for the water flow
are the downstream component of gravitaty force and the xmomentum carried by the
impacting raindrops. We shall (for simplicity) assume that the frictional resistance at the
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 Fall '05
 GarethMcKinley

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