Question

a piston having a cross sectional area of .07m^2 is located ina cylinder containing water. an open utube manometer is connected to a cylinder

Answer 1

The water column height in the open U-tube manometer connected to the cylinder is determined by the pressure difference between the atmosphere and the water in the cylinder. The pressure difference can be calculated using the equation
`\( \Delta P = \rho \cdot g \cdot h \)`, where
`\( \rho \)` is the density of water,
`\( g \)`is the acceleration due to gravity, and
`\( h \)` is the height difference in the manometer arms.

Step-by-step explanation:

In this scenario, the cross-sectional area of the piston is
`\( A = 0.07 \, \text{m}^2 \).` The force exerted by the piston due to the water pressure is given by
`\( F = P \cdot A \).` This force is balanced by the weight of the water column in the manometer,
`\( W = \rho \cdot g \cdot h \cdot A_{\text{mano}} \),` where
`\( A_{\text{mano}} \)`is the cross-sectional area of the manometer tubes. Setting these equal and rearranging, we get
`\( P = \rho \cdot g \cdot h_{\text{mano}} \), where \( h_{\text{mano}} \)` is the height difference in the manometer.

By substituting this expression for
`\( P \)` into the pressure difference equation
`\( \Delta P = \rho \cdot g \cdot h \),` we find
`\( h_{\text{mano}} = (\Delta P)/(\rho \cdot g) \).` Now, plugging in the given values and constants, we can calculate the height difference
`\( h_{\text{mano}} \)` and determine the water column height in the open U-tube manometer.

This process utilizes the principles of fluid mechanics and the equilibrium of forces to relate the pressure difference in the cylinder to the height difference in the manometer, allowing for the calculation of the water column height.