Water passes through a pump. At the suction flange, gauge pressure is $p_1=-20.0\text{ kPa}$, velocity is $V_1=2.00\text{ m/s}$, and elevation is $z_1=0$. At the discharge flange, $p_2=250\text{ kPa}$, $V_2=3.00\text{ m/s}$, and $z_2=5.00\text{ m}$. Take $\alpha_1=\alpha_2=1$ and $\gamma=9.81\text{ kN/m}^3$. Determine pump total head.

A pump delivers $50.0\text{ L/s}$ of water against a total dynamic head of $40.0\text{ m}$. Pump efficiency is $75.0\%$ and motor efficiency is $90.0\%$. Determine water power, shaft power, and electrical input power.

A pump delivers $0.0800\text{ m}^3/\text{s}$ against $25.0\text{ m}$ head while absorbing $30.0\text{ kW}$ of shaft power. Determine pump efficiency.

A pump curve is approximated by $H_p=50-0.020Q^2$ and the connected system by $H_{\text{sys}}=10+0.010Q^2$, with $H$ in metres and $Q$ in $\text{L/s}$. Determine the operating flow and head.

Each pump has $H=40-0.010Q^2$, where $H$ is in metres and $Q$ in $\text{L/s}$. The system curve is $H_{\text{sys}}=20+0.015Q^2$. Determine the operating point for two identical pumps in series.

Each pump has $H=50-0.020q^2$, where $q$ is one-pump discharge in $\text{L/s}$. The system curve is $H_{\text{sys}}=10+0.010Q^2$, where $Q$ is total station discharge. Determine the operating point for two identical pumps in parallel.

At $1200\text{ rpm}$ a pump curve is $H_p=40-0.010Q^2$, with $H$ in metres and $Q$ in $\text{L/s}$. The system curve is $H_{\text{sys}}=5+0.005Q^2$. Estimate the operating point at $1200\text{ rpm}$ and after reducing speed to $900\text{ rpm}$.

A centrifugal pump at constant speed delivers $Q_1=0.100\text{ m}^3/\text{s}$ at $H_1=30.0\text{ m}$ and absorbs $P_1=40.0\text{ kW}$ with impeller diameter $D_1=300\text{ mm}$. Estimate performance after a modest trim to $D_2=270\text{ mm}$.

A pump draws water from an open reservoir. Atmospheric pressure head is $10.3\text{ m}$ of water, vapor-pressure head is $0.240\text{ m}$, the pump centerline is $3.00\text{ m}$ above the reservoir surface, and suction-line loss is $1.20\text{ m}$. Determine $NPSH_A$ and compare it with $NPSH_R=4.20\text{ m}$.

At a higher-elevation, warmer installation, atmospheric pressure head is $8.50\text{ m}$, vapor-pressure head is $0.500\text{ m}$, suction lift is $2.00\text{ m}$, and suction loss is $1.00\text{ m}$. The pump has $NPSH_R=4.50\text{ m}$ at the proposed flow. Determine $NPSH_A$ and the numerical excess above $NPSH_R$.

A pump operates at $N=1450\text{ rpm}$, $Q=0.100\text{ m}^3/\text{s}$, and $H=30.0\text{ m}$ at BEP. Calculate the conventional metric index $N_s=N\sqrt{Q}/H^{3/4}$ and the dimensionless pump specific speed $\Omega_s=\omega\sqrt Q/(gH)^{3/4}$.

For a centrifugal pump, inlet whirl is negligible so $V_{\theta1}=0$. At the impeller outlet, blade speed is $u_2=20.0\text{ m/s}$ and tangential absolute velocity is $V_{\theta2}=15.0\text{ m/s}$. Determine ideal Euler head. If hydraulic efficiency relative to Euler head is $85.0\%$, estimate actual developed head.

A turbine receives $3.00\text{ m}^3/\text{s}$ of water under net head $H_n=40.0\text{ m}$. Turbine efficiency is $90.0\%$ and generator efficiency is $96.0\%$. Determine shaft power and electrical output.