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The pressure at depth h below the surfac...

The pressure at depth h below the surface of a liquid of density `rho` open to the atmosphere is

A

greater than the atmospheric pressure by `rhogh`

B

less than the atmospheric pressure by `rhogh`

C

equal to the atmospheric pressure

D

increases exponentially with depth

Text Solution

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The correct Answer is:
To find the pressure at a depth \( h \) below the surface of a liquid with density \( \rho \) that is open to the atmosphere, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Scenario**: - We have a liquid that is open to the atmosphere. - The liquid has a density \( \rho \). - We need to determine the pressure at a depth \( h \) below the surface of this liquid. 2. **Identify the Atmospheric Pressure**: - The pressure at the surface of the liquid (where it is open to the atmosphere) is the atmospheric pressure, denoted as \( P_A \). 3. **Apply the Hydrostatic Pressure Formula**: - The pressure due to a column of liquid at a depth \( h \) is given by the formula: \[ P_{\text{liquid}} = \rho g h \] - Here, \( g \) is the acceleration due to gravity. 4. **Calculate the Total Pressure at Depth \( h \)**: - The total pressure \( P \) at depth \( h \) is the sum of the atmospheric pressure and the pressure due to the liquid column: \[ P = P_A + \rho g h \] 5. **Conclusion**: - Therefore, the pressure at depth \( h \) below the surface of the liquid is: \[ P = P_A + \rho g h \] ### Final Answer: The pressure at depth \( h \) below the surface of a liquid of density \( \rho \) open to the atmosphere is given by: \[ P = P_A + \rho g h \]
To find the pressure at a depth \( h \) below the surface of a liquid with density \( \rho \) that is open to the atmosphere, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Scenario**: - We have a liquid that is open to the atmosphere. - The liquid has a density \( \rho \). - We need to determine the pressure at a depth \( h \) below the surface of this liquid. ...
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