The pressure experienced by a swimmer $20 ext{ m}$ below the water surface in a lake is appropriately: (Give

Question

The pressure experienced by a swimmer $20 	ext{ m}$ below the water surface in a lake is appropriately: (Given density of water = $10^3 	ext{ kg m}^{-3}$, $g=10 	ext{ m s}^{-2}$ and $1 	ext{ atm} = 10^5 	ext{ Pa}$)

Accepted Answer

The total (absolute) pressure experienced by the swimmer is the sum of the atmospheric pressure acting on the surface and the gauge pressure due to the water column above.

1.  **Formula:** $P_{total} = P_{atm} + ho g h$
2.  **Calculate Gauge Pressure ($P_{gauge}$):**
    $$P_{gauge} = ho g h$$
    Substituting the given values: $ho = 10^3 	ext{ kg m}^{-3}$, $g = 10 	ext{ m s}^{-2}$, $h = 20 	ext{ m}$.
    $$P_{gauge} = 10^3 	imes 10 	imes 20 = 2 	imes 10^5 	ext{ Pa}$$
3.  **Convert to Atmospheres:**
    Given $1 	ext{ atm} = 10^5 	ext{ Pa}$.
    $$P_{gauge} = \frac{2 	imes 10^5}{10^5} 	ext{ atm} = 2 	ext{ atm}$$
4.  **Calculate Total Pressure:**
    $$P_{total} = 1 	ext{ atm} (	ext{atmospheric}) + 2 	ext{ atm} (	ext{due to depth}) = 3 	ext{ atm}$$

Step-by-Step Solution

Practice All PHYSICS Questions