A liquid has mass $18.0\text{ kg}$ in a volume of $0.0150\text{ m}^3$. Determine its density and specific gravity relative to water at $1000\text{ kg/m}^3$.

Fresh water of density $1000\text{ kg/m}^3$ fills a pool to a depth of $3.00\text{ m}$. Atmospheric pressure is $101\text{ kPa}$. Determine the gauge and absolute pressures at the bottom using $g=9.81\text{ m/s}^2$.

A hydraulic lift has a small piston radius of $2.00\text{ cm}$ and a large piston radius of $15.0\text{ cm}$. Determine the small-piston force needed to support a $1500\text{ kg}$ car using $g=9.80\text{ m/s}^2$.

An open U-tube contains mercury of density $13{,}600\text{ kg/m}^3$. A $0.150\text{ m}$ water column stands above the mercury-water interface in the right arm. Determine how far the mercury free surface in the left arm lies above that interface.

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A vertical rectangular gate in fresh water is $2.00\text{ m}$ high and $1.50\text{ m}$ wide. Its centroid is $5.00\text{ m}$ below the free surface. Determine the hydrostatic resultant and center-of-pressure depth.

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An aluminum block of volume $0.0500\text{ m}^3$ is completely submerged in fresh water. Determine the buoyant force using $g=9.80\text{ m/s}^2$.

Ice has density $917\text{ kg/m}^3$ and seawater has density $1025\text{ kg/m}^3$. Determine the fraction of a freely floating iceberg that is submerged.

Water flows at $2.00\text{ m/s}$ through a horizontal pipe of radius $4.00\text{ cm}$ that contracts to radius $2.00\text{ cm}$. Determine the downstream speed.

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For the same horizontal pipe, the upstream absolute pressure is $150\text{ kPa}$, with $v_1=2.00\text{ m/s}$ and $v_2=8.00\text{ m/s}$. Determine downstream absolute pressure for water of density $1000\text{ kg/m}^3$, neglecting losses.

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Water flows through a horizontal pipe with $p_1=200\text{ kPa}$ gauge, $v_1=2.00\text{ m/s}$, $v_2=4.00\text{ m/s}$, and head loss $h_L=1.00\text{ m}$. Determine $p_2$ using $\rho=1000\text{ kg/m}^3$ and $g=9.81\text{ m/s}^2$.

A large open water tank has a small side opening $5.00\text{ m}$ below its free surface. Determine the ideal exit speed, neglecting losses and free-surface velocity.

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