An-open-pipe-of-r-o-10-Cm-3m-has-an-outer-layer-of-ice-that-is-melting-at-the-rate-of-2pi-Cm-3-per-minute-with-thickness-of-20-mm-How-many-days-untill-all-the-ice-melts-and-how-fast-is-the-

Question Number 181053 by Acem last updated on 22/Nov/22

A n o p e n p i p e o f r_{o} = 10 C m, ℓ = 3 m h a s a n o u t e r

l a y e r o f i c e t h a t i s m e l t i n g a t t h e r a t e o f 2 π {C m}^{3}

p e r m i n u t e w i t h t h i c k n e s s o f 20 m m . H o w m a n y

d a y s u n t i l l a l l t h e i c e m e l t s ? a n d h o w f a s t i s t h e

t h i c k n e s s o f t h e i c e d e c r e a s i n g p e r h o u r ?

Answered by Acem last updated on 22/Nov/22

V_{i c e} = π ℓ [{(r_{o} + δ)}^{2} - r_{o}^{2}]; δ : t h i c k n e s s o f t h e i c e l a y e r

\frac{\partial V}{\partial t} = 2 π ℓ (r_{o} + δ) \frac{\partial δ}{\partial t} = - 2 π

\frac{\partial δ}{\partial t} = - 0.16 m m / h r t h e r a t e o f t h e i c e i s d e c r e a s i n g

H e n c e 4 m m p e r d a y

T h e n i t t a k e s 5 d a y s t o f u l l y m e l t

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