So Far: Mass and Volume Flow Rates Reynolds No., Laminar/Turbulent Pressure Drop in Pipes

1. So Far: Mass and Volume Flow Rates Reynolds No., Laminar/Turbulent Pressure Drop in Pipes Flow Measurement, Valves Total Head, Pump Power, NPSH This Week: Bernoulli’s Equation and its Application Pump Sizing, Types of Pumps Conservation of Energy

2. Pump Sizing • Volume Flow Rate (m3/hr or gpm) • Total Head, h (m or ft) • 2a. P (bar, kPa, psi) • Power Output (energy added to fluid) and Input (mechanical shaft power from motor) • NPSH Required

3. Pumps Centrifugal Impeller spinning inside fluid Kinetic energy to pressure Flow controlled by Pdelivery Positive Displacement Flow independent of Pdelivery Many configurations

4. Centrifugal Pumps Delivery Impeller Volute Casting Suction

5. Centrifugal Pumps Flow accelerated (forced by impeller) Then, flow decelerated (pressure increases) Low pressure at center “draws” in fluid Pump should be full of liquid at all times Flow controlled by delivery side valve May operate against closed valve Seal between rotating shaft and casing

6. Centrifugal Pumps Advantages Simple construction, many materials No valves, can be cleaned in place Relatively inexpensive, low maintenance Steady delivery, versatile Operates at high speed (electric motor) Wide operating range (flow and head) Disadvantages Multiple stages needed for high pressures Poor efficiency for high viscosity fluids Must prime pump

7. Centrifugal Pumps H-Q Chart Increasing Impeller Diameter Head (or P) A B C Volume Flow Rate

8. Centrifugal Pumps H-Q Chart Increasing Efficiency Head (or P) Required NPSH A B C Volume Flow Rate

9. Centrifugal Pumps H-Q Chart Head (or P) A B C Volume Flow Rate

10. Centrifugal Pumps H-Q Chart Required Flow Capacity Head (or P) Actual Flow Capacity Required Power Volume Flow Rate

11. Centrifugal Pumps What if available NPSH is less than required NPSH? Increase Available NPSH 1. Increase suction static head (pump location) 2. Increase suction side pressure 3. Decrease fluid vapor pressure 4. Reduce friction losses on suction side Decrease Required NPSH 1. Reduce pump speed 2. Select a different pump

12. Centrifugal Pumps Curves created for specific speed, viscosity and density Often, use more charts or correction factors to “fine tune” pump selection Variable speed motor has same effect as impeller size Multiple pump/impeller combinations may work

13. Centrifugal Pumps Closed Impeller Most common, low solids Water, beer, wort Flash pasteurization Refrigerants Open Impeller Lower pressures Solids okay Mash to lauter turn Liquid yeast, wort, hops

14. Positive Displacement Pumps Theory: Volume dispensed independent of delivery head Practice: As delivery head increases, some slippage or leakage occurs Speed used to control flow rate, use of valves could cause serious damage Self-priming Good for high viscosities, avoiding cavitation

15. Positive Displacement Pumps Piston Pump Volumetric Efficiency High Pressures Metering hop compounds, detergents, sterilents Suction Valve Delivery Valve

16. Positive Displacement Pumps Peristaltic Pump

17. Positive Displacement Pumps Gear Pump High Pressures No Pulsation High Viscosity Fluids No Solids Difficult to Clean

18. Positive Displacement Pumps Lobe Rotor Pump Both lobes driven Can be sterilized Transfer Yeast Trub Bulk Sugar Syrup

19. Conservation of Energy • For steady flow systems • Energy = Heat (Q), Work (W), mass (h) • No Phase Change, E = m c ΔT • Phase Change, E = m hfg where • hfg = enthalpy of vaporization or fusion

20. A 2 m3 water tank is filled with 1.25 m3 of hot water at 80C and 0.75 m3 of cold water at 10C. Assume that the specific heat of water is 4.2 kJ/kg.K. • Determine the temperature in the tank after it has been filled. • How much heat must be added to the tank to bring its temperature to 65C? • If a 30 kW electric heater is used, how long will the heating process take?

21. 500 kg of grain (25C) is mixed with hot (80C) and cold (10C) water for mashing. The water to grain ratio (by weight) is 3:1 and the specific heat capacities of the water and grain are 4.2 and 1.7 kJ/kg.K, respectively. a) If the desired “mash in” temperature is 38C, how much hot and cold water should be added?

22. (Continued) A three step mashing process, with 20 minute-long rests at 50, 62 and 72C, is desired. The mash should be heated quickly, but not too quickly between rests; with an optimal rate of 1C per minute. Neglect heat losses to the surroundings. b) Plot the mash temperature vs. time. c) Determine the heating power required, in kW. d) Determine the total heat required for the mashing process, in kJ.

23. Two types of heat sources are available for mashing, electric resistance heaters and steam. The steam enters a heating jacket around the mash as dry, saturated steam at 300 kPa and it exits the system as wet, saturated steam at the same pressure (enthalpy of vaporization = 2150 kJ/kg). (e) What is steam flow rate required, in kg/s? (f) If steam is used, what is the total mass of steam required, in kg?

24. At the location of our brewery, electricity costs $0.14/kW-hr and the steam can be generated for $0.03 per kg. (g) What is the mashing cost when electric resistance heaters are used? (h) What is the cost with steam?