A marine-biology laboratory places a pressure probe at the bottom of an estuary where…

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Fluids · Fluids

Problem

A marine-biology laboratory places a pressure probe at the bottom of an estuary where the water has salinity-dependent density

\rho = 1.020\times10^{3}\,\text{kg}\,\text{m}^{-3}

. The probe measures a gauge pressure of

1.60\times10^{5}\,\text{Pa}

. A student calculates the corresponding depth using

g = 9.80\,\text{m}\,\text{s}^{-2}

, whereas the local gravitational acceleration is actually

g_{\text{true}} = 9.78\,\text{m}\,\text{s}^{-2}

. Atmospheric pressure at the estuary surface is

1.01\times10^{5}\,\text{Pa}

. (a) Calculate the depth obtained by the student using

g = 9.80\,\text{m}\,\text{s}^{-2}

. (b) Re-calculate the true depth using

g_{\text{true}} = 9.78\,\text{m}\,\text{s}^{-2}

. (c) Determine the percent error introduced by the student’s approximation of

g

. (d) Discuss whether this percent error is significant for engineering applications that require depth measurements within

\pm0.5\,\%

accuracy, and justify your answer.