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14.76:
a) The change in pressure with respect to the vertical distance supplies the force
necessary to keep a fluid element in vertical equilibrium (opposing the weight). For the
rotating fluid, the change in pressure with respect to radius supplies the force necessary to
keep a fluid element accelerating toward the axis; specifically,
,
ρa dr
dr
dp
p
p
=
=
∂
∂
and
using
r
ω
a
2
=
gives
.
2
r
ρω
p
p
=
∂
∂
b) Let the pressure at
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Unformatted text preview: , = = r y be a p (atmospheric pressure); integrating the expression for p p ∂ ∂ from part (a) gives ( 29 . 2 2 a 2 , r ρω p y r p + = = c) In Eq. ) , ( , ), 5 . 14 ( 1 a 2 = = = y r p p p p as found in part (b), ), ( y and 2 1 r h y = = the height of the liquid above the = y plane. Using the result of part (b) gives . 2 ) ( 2 2 g r ω r h =...
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- Euclidean geometry, fluid element
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