Question

If $ P_0 $ is the atmospheric pressure and $ P $ is the pressure at a depth $ h $, find the Guage pressure.

• A. \( P - P_0 \)
• B. \( P_0 - P \)
• C. \( P_0 \times P \)
• D. \( P \times h \)

Hint:

The gauge pressure is always measured relative to the atmospheric pressure. Subtract the atmospheric pressure from the total pressure to get the gauge pressure.

Answer 1

The Correct Option is A

The gauge pressure is the difference between the pressure at a given depth \( h \) and the atmospheric pressure. The atmospheric pressure \( P_0 \) is the pressure at sea level, and the pressure \( P \) at depth is the sum of the atmospheric pressure and the water pressure due to the column of water above. Therefore, the gauge pressure, \( P_g \), is given by: \[ P_g = P - P_0 \] This formula gives the pressure that is in excess of the atmospheric pressure at that depth.
Thus, the correct answer is \( P - P_0 \).