First slide

Pressure in a fluid-mechanical properties of fluids

Question

A tube 1 cm² in cross section is attached to the top of a vessel 1 cm high and of cross section 100 cm². Water is poured into the system filling it to a depth of 100 cm above the bottom of the vessel as shown in the figure. Take g=10 ms^-2. Find the correct statement.

Moderate

A

The force exerted by water against the bottom of the vessel is 100 N
B

The weight of water in the system is 1.99 N.
C

Both (a) and (b) are correct.
D

Neither (a) nor (b) is correct.

Solution

Pressure due to water at the bottom of vessel is
$P = h ρ g = 1 m \times 1000 k g m^{- 3} \times 10 {ms}^{- 2} = 10^{4} P a$
Force due to water at the bottom of vessel is
$F = P A = 10^{4} P a \times 100 \times 10^{- 4} m^{2} = 100 N$
$Volume of water= V = (99 c m \times 1 c m^{2}) + (1 c m \times 100 c m^{2}) = 199 {cm}^{3} M a s s = M = ρ V = (1 g c m^{- 3}) (199 {cm}^{3}) = 199 g = 0.199 k g W e i g h t = M g = 0.199 \times 10 = 1.99 N$

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