Question

5. The pressure at the free surface of a water lake is P1
and that at a point at depth h below its free surface is
P2.
(a) Which is more, P1 or P2, and why?
(b) How are P1 and P2 related to?
Plz give its solution as soon as possible ​

Answer 1

Given:

The pressure at the free surface of a water lake is P1 and that at a point at depth h below its free surface is P2.

To find:

• Which is more P1 or P2 ?
• Relationship between P1 and P2 ?

Calculation:

At the free surface of the lake the net pressure is actually the pressure exerted by atmosphere. Hence, it will be atmospheric pressure represented by P_(atm)

$\boxed{ \therefore \: P_{1} = P_{atm}}$

Now , when we move to a depth "h" below the the free surface of the lake , the net pressure increases because the total pressure at that point is contributed by both atmospheric pressure as well as the column of water present above that point.

• General expression of pressure at a depth D from the surface of a liquid is given as follows: P = $\rho \times g \times D$

So, total pressure at depth "h":

$\boxed{ \therefore \: P_{2} = P_{atm} + \rho gh}$

So , we can say that : P2 > P1.

Now , relationship between P1 and P2:

$= > \: P_{2} = P_{atm} + \rho gh$

$= > \: P_{2} = P_{1} + \rho gh$

So, required relationship is:

$\boxed{ \bold{\: P_{2} = P_{1} + \rho gh}}$

Hope It Helps.

Answer 2

Answer:

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