Question

A lake has a maximum depth of 60 m. If the mean atmospheric pressure in the lake region is 91 kPa and the unit weight of the lake water is 9790 N/m\(^3\), the absolute pressure (in kPa, round off to two decimal places) at the maximum depth of the lake is \(\underline{\hspace{2cm}}\).

Hint:

The absolute pressure at a depth is the sum of the atmospheric pressure and the pressure due to the water column.

Answer 1

Correct Answer: 677.5 - 679.5

The absolute pressure at the maximum depth is given by the formula: \[ P_{\text{absolute}} = P_{\text{atmospheric}} + \gamma \times h, \] where \( P_{\text{atmospheric}} = 91 \, \text{kPa} \), \( \gamma = 9790 \, \text{N/m}^3 \), and \( h = 60 \, \text{m} \). Thus: \[ P_{\text{absolute}} = 91 + \frac{9790 \times 60}{1000} = 91 + 587.4 = 678.4 \, \text{kPa}. \] Thus, the absolute pressure at the maximum depth is \( \boxed{678.4} \, \text{kPa} \).