Hydrostatics: Pressure & Manometry — Worked Examples

Seawater has $SG=1.03$. Determine the absolute pressure $15.0\ \text{m}$ below an open surface when local atmospheric pressure is $101.3\ \text{kPa}$. Use $\gamma_w=9.81\ \text{kN/m}^3$.

A gage pressure is $196.2\ \text{kPa}$. Express it as metres of water and metres of mercury. Use $\gamma_w=9.81\ \text{kN/m}^3$ and $SG_{Hg}=13.6$.

A mercury barometer reads $742\ \text{mm}$. Take $SG_{Hg}=13.6$ and neglect mercury vapor pressure. Determine local atmospheric pressure.

A hydraulic press has a $50.0\ \text{mm}$ diameter input piston and a $400\ \text{mm}$ diameter output piston. Neglect elevation differences and mechanical losses. Determine the output force produced by a $500\ \text{N}$ input force and the output displacement if the input piston moves $80.0\ \text{mm}$.

An open piezometer connected to a water main shows a water level $4.50\ \text{m}$ above the pipe tap. Determine the gage pressure at the connection.

A water pipe is connected to one leg of a mercury U-tube; the other mercury leg is open to atmosphere. The pipe tap and the open mercury free surface are at the same elevation. The water-mercury interface on the pipe side is $0.180\ \text{m}$ below that elevation. Find the pipe gage pressure using $SG_{Hg}=13.6$.

An inclined manometer containing oil with $SG=0.85$ measures the pressure difference between two gas spaces whose gas-column weight is negligible. The liquid-interface displacement is $0.400\ \text{m}$ along a tube inclined $30.0^\circ$ above horizontal. Determine the vertical head and pressure difference.

A differential manometer connects pipe A containing water to pipe B containing oil with $SG=0.80$. Mercury with $SG=13.6$ is the manometric fluid. Starting at A, move downward $0.500\ \text{m}$ in water to the left mercury interface, upward $0.200\ \text{m}$ in mercury to the right interface, and upward $0.300\ \text{m}$ in oil to B. Determine $p_A-p_B$.

An open tank contains $2.00\ \text{m}$ of oil with $SG=0.80$ above $3.00\ \text{m}$ of water. Determine bottom gage pressure.

A vessel gage reads $-62.0\ \text{kPa}$ while local atmospheric pressure is $98.0\ \text{kPa}$. Determine absolute pressure and vacuum-pressure magnitude.