Problem 1: Bernoulli Flow through a Horizontal Contraction

Water flows through a horizontal pipe. Section 1 has diameter $150\text{ mm}$ and pressure $200\text{ kPa}$; Section 2 has diameter $75\text{ mm}$ and pressure $100\text{ kPa}$. Neglect losses and determine discharge.

Problem 2: Ideal Jet from a Reservoir Nozzle

A nozzle of diameter $50\text{ mm}$ discharges water from a large reservoir. The nozzle center is $5.0\text{ m}$ below the free surface. Neglect losses and determine jet velocity and discharge.

Problem 3: Pump Head and Input Power

A pump transfers water between reservoirs whose surfaces differ in elevation by $30\text{ m}$. The discharge is $0.050\text{ m}^3/\text{s}$, total head loss is $5\text{ m}$, and pump efficiency is $80\%$. Determine pump head and input power.

Problem 4: Turbine Power from a Pipeline

Water flows at $2.0\text{ m}^3/\text{s}$ from an upper reservoir to a lower reservoir $25\text{ m}$ below. Pipeline losses are $3\text{ m}$ and turbine efficiency is $85\%$. Determine turbine output power.

Problem 5: Pressure at a Siphon Crest

A siphon crest is $6.0\text{ m}$ above the source reservoir surface. Water velocity at the crest is $3.0\text{ m/s}$ and head loss from the reservoir to the crest is $0.50\text{ m}$. Atmospheric pressure is $101.3\text{ kPa}$ absolute. Determine crest gauge and absolute pressure.

Problem 6: Pitot-Static Velocity Measurement

A Pitot-static tube in air measures a stagnation-minus-static pressure of $3.5\text{ kPa}$. Air density is $1.20\text{ kg/m}^3$. Determine velocity, assuming incompressible behavior.

Problem 7: Axial Force on a Reducing Nozzle

A horizontal nozzle contracts from $100\text{ mm}$ to $50\text{ mm}$ diameter. Water discharge is $0.020\text{ m}^3/\text{s}$, inlet gauge pressure is $200\text{ kPa}$, and the outlet jet is atmospheric. Neglect weight and determine the force of water on the nozzle.

Problem 8: Force on a 90-Degree Elbow

A horizontal $150\text{ mm}$ diameter elbow turns water flow $90^\circ$ from the positive x-direction to the positive y-direction. $Q=0.050\text{ m}^3/\text{s}$, $p_1=150\text{ kPa}$ gauge, and $p_2=120\text{ kPa}$ gauge. Neglect weight. Determine the force of the water on the elbow.