A diver is swimming at a depth of 3.5\text{ m} below the surface of a freshwater lake. If … — JAMB UTME

A diver is swimming at a depth of $3.5\text{ m}$ below the surface of a freshwater lake. If the density of water is $1000\text{ kg/m}^3$ and the acceleration due to gravity $g = 10\text{ m/s}^2$ , what is the gauge pressure exerted on the diver in pascals?

Answer: 35000 Pa

Answer

35000 Pa

The gauge pressure exerted by a static column of fluid is given by

P = h \rho g

. Using the values

h = 3.5\text{ m}

\rho = 1000\text{ kg/m}^3

, and

g = 10\text{ m/s}^2

, the pressure is

P = 3.5 \times 1000 \times 10 = 35000\text{ Pa}

Step-by-Step Solution

Identify the formula for liquid hydrostatic pressure

P = h \rho g

Gauge pressure at a depth

h

in a static fluid depends on depth, fluid density, and gravitational field strength.

Substitute the given numerical values

P = 3.5 \times 1000 \times 10

Substitute depth

h = 3.5\text{ m}

, density

\rho = 1000\text{ kg/m}^3

, and

g = 10\text{ m/s}^2

Perform the multiplication to determine the pressure

35000\text{ Pa}

Complete the calculation to get the pressure in SI units (Pascals).

Key Concept

Hydrostatic Pressure in Static Fluids

Estimated Time:45s

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