Question

The maximum depth for recreational scuba diving is considered $130\text{ft}$. If a diver's suit is specially designed to bear water pressure $15\%$ more than that exerted at the maximum allowable diving depth:

1. Calculate the water pressure exerted on the diver at the maximum allowable depth. $\left[2\text{marks}\right]$
2. How deeper can the diver dive with the specially designed diving suit? $\left[3\text{marks}\right]$

Take the density of the seawater to be $1025{\text{kg/m}}^3$.

Answer 1

Given:
The maximum allowable depth for recreational scuba diving, ${\text{h}}_1=130\text{ft}\approx 40\text{m}$
The density of the seawater, ${\rho }_{\text{sw}}=1025{\text{kg/m}}^3$

1. The pressure felt by the diver at the maximum allowable depth would be ${\text{P}}_1={\rho }_{\text{sw}}g{\text{h}}_1$ $=1025\times 10\times 40=410000\text{Pa}=410\text{kPa}$ $\left[2\text{marks}\right]$
2. The diver's special suit enables $15\%$ more pressure-bearing capacity $⟹$ new pressure $\left({\text{P}}_2\right)=1.15{\text{P}}_1=471500\text{Pa}$ The depth to which the diver can dive in this case ${\text{h}}_2=\frac{471500}{1025\times 10}=46\text{m}$ Therefore, the diver can dive $6\text{m}$ deeper than the maximum allowable depth with the special suit. $\left[3\text{marks}\right]$