9. FLUID FLOW: Working Problems CH EN 170

Fluid Flow Schedule Today Thursday Next Tuesday Next Thursday Short exam review Examples of working problems with the mechanical energy equation Thursday Pumps Efficiency, pump curves, power Next Tuesday ChemE Car Project Introduction Next Thursday Balances quiz for points back on exam (up to a total grade of 75)

Mechanical Energy Balance 𝑃 2 − 𝑃 1 𝜌 + 1 2 𝛼 𝑣 2 2 − 𝑣 1 2 +𝑔( 𝑧 2 − 𝑧 1 )= 𝑤 𝑠 − 𝑤 𝑓

Example: Pressure across a nozzle Liquid with a density of 500 kg/m3 flows at steady state through a horizontal nozzle before hitting the atmosphere. If at the start of the nozzle the diameter is 2 cm and the velocity is 1 m/s, and at the end of the nozzle the diameter is 1 cm, what is the pressure at the start of the nozzle? (Assume friction is insignificant)

Pressure drop In almost all pipe systems, pressure falls in the direction of flow. This is called a “pressure drop.” The bigger pressure at the beginning presses the fluid through the pipe.

Example: Friction A pressure drop along a 1-cm diameter horizontal pipe in which water is flowing at a steady state of 1 m/s is measured as 70 kPa. What is the value of friction per mass of fluid (wf) in J/kg. Hint: 𝜌 𝑤𝑎𝑡𝑒𝑟 =1000 𝑘𝑔/ 𝑚 3

Friction and pressure drop Usually, there is more friction in a long, narrow pipe or tube. Friction has a large effect on the pressure drop (the more energy lost to friction, the bigger the pressure drop).

Siphon Set-up

Example: Falling Fluid A 10 meter tall and 10 meter in diameter cylindrical water tower sits 40 meters above ground water filled to the top, but is not pressurized. What is the velocity of water from a shower (6 ft above ground level) in the town below the water tower, assuming negligible friction and no other energy losses along the way?

Example: Gripper (From Lab) In the Venturi gripper you played with in your lab last week, fluid (water or air) flows from a plastic tube through the opening of the gripper at a constant of rate 𝑉 . A disk of diameter D is held up against the flow. Use the mechanical energy equation for a gripper with air flowing through to show why the disk doesn’t fall.