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Laws of Liquid Pressure

Q.Show that t...

Question

Q.Show that the pressure P at a depth h from the free surface of a liquid in container is P = $P_{0}$ +h $ρ$ g , where $P_{0}$ is the atmospheric pressure, $ρ$ is the density of liquid and g is acceleration due to gravity.

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Solution

$D e a r s t u d e n t, L e t u s c a l c u l a t e t h e p r e s s u r e e x e r t e d o n t h e b o t t o m b y t h e w e i g h t o f t h e f l u i d . P = \frac{m g}{A} W e c a n f i n d t h e m a s s o f t h e f l u i d f r o m i t s v o l u m e a n d d e n s i t y : m = ρ V T h e v o l u m e o f t h e f l u i d V i s r e l a t e d t o t h e d i m e n s i o n s o f t h e c o n t a i n e r . I t i s V = A h w h e r e A i s t h e c r o s s - s e c t i o n a l a r e a a n d h i s t h e d e p t h . C o m b i n i n g t h e l a s t t w o e q u a t i o n s g i v e s m = ρ A h s o, P = \frac{ρ A h \times g}{A} P = ρ g h I f w e c o m b i n e a t m o s p h e r i c p r e s s u r e t h e n, P = P_{o} + ρ g h R e g a r d s$

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