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Question

# Determine the pressure exerted on a diver at 20 m below the free surface of the sea. Assume a barometric pressure of 101 kPa and a specific gravity of 1.03 for seawater.

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Given:

\begin{aligned} h&=&20\:\text{m}\rightarrow\text{Height}\\ p_b&=&101\:\text{kPa}\rightarrow\text{Barometric pressure}\\ SG&=&1.03\rightarrow\text{Specific gravity of sea water} \end{aligned}

We assume density of water $\rho_w=1000\:\frac{\text{kg}}{\text{m}^3}$

Density for sea water is defined by specific gravity of sea water and density of water:

$\begin{equation*} \rho_s=SG\cdot\rho_w=1.03\cdot1000\:\frac{\text{kg}}{\text{m}^3}=1030\:\frac{\text{kg}}{\text{m}^3} \end{equation*}$

The pressure on distance $h=20\:\text{m}$ to free surface of water is defined by biometric pressure and height $h$.

\begin{aligned} p&=&p_b+\rho\cdot g\cdot h=101\:\text{kPa}+1030\:\frac{\text{kg}}{\text{m}^3}\cdot9.81\:\frac{\text{m}}{\text{s}^2}\cdot\frac{\text{kPa}}{1000\text{Pa}}\\ p&=&\boxed{303\:\text{kPa}} \end{aligned}

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