Download Presentation
## Mass Rate Balance

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**ME 200 L14:Conservation of Mass: Control Volume 4.1-4.3 HW 5**cancelled HW 6 assigned https://engineering.purdue.edu/ME200/Spring 2014 MWF 1030-1120 AMJ. P. Gore gore@purdue.eduGatewood Wing 3166, 765 494 0061Office Hours: MWF 1130-1230TAs: Robert Kapaku rkapaku@purdue.edu Dong Han han193@purdue.edu**time rate of change of**mass contained within the control volume attime t time rate of flow of mass in across inlet i attime t time rate of flow of mass out across exit e attime t (Eq. 4.1) Mass Rate Balance**(Eq. 4.2)**Mass Rate Balance In practice there may be several locations on the boundary through which mass enters or exits. Multiple inlets and exits are accounted for by introducing summations: Eq.4.2 is the mass rate balance for control volumes with several inlets and exits.**(Eq. 4.4b)**where V is velocity v is specific volume Mass Flow Rate(One-Dimensional Flow) • Flow is normal to the boundary at locations where mass enters or exits the control volume. • All intensive properties are uniform with position over each inlet or exit area (A) through which matter flows.**How long does a 50 gallon drum take to fill if H2O is added**at 2 gallons/minute and density remains constant? If a 2 inch hose is currently feeding the water, find the average velocity of water in the hose. If the time to fill needs to be reduced to 25%, and only one hose can be used, what size hose would be needed? Control Volume Basic Equations Solution 1 Water 2 Example**(Eq. 4.6)**(mass rate in) (mass rate out) Mass Rate Balance(Steady-State Form) • Steady-state: all properties are unchanging in time. • For steady-state control volume, dmcv/dt = 0.**R 134a enters the condenser of a refrigeration system**operating at steady state and 9 bar, 50 ºC, through a 2.5 cm diameter pipe. At the exit, the pressure is 9 bar, the temperature is 30 ºC, and the velocity is 2.5 m/s. The mass flow rate of the entering refrigerant is 6 kg/min. Determine: the velocity at the inlet, in m/s, and the diameter of the exit pipe, in cm. Find V1 = ? in m/s d2 = ? in cm System Basic Equations Solution 1 • P1 = 9 bar • T1 = 50 ºC • d1 = 2.5 cm • m1 = 6 kg/min • P2 = 9 bar • T2 = 30 ºC • V2 = 2.5 m/s R-134a 2 Example 6 kg/min = π/4(0.025 m)2 V/0.0247 m3/kg V1 = 5.03 m/s d2 = 2.07 cm**A direct contact feed-water heater is shown in the sketch.**Water at 7 bars and 40 C enters through a 25 cm2 port and is heated by steam entering at 7 bars and temperature of 200 C at a flow rate of 40 kg/s. The resulting saturated liquid leaves the FWH at 7 bars. Find: Mass flow rate at inlet 2 and exit 3. Assumptions: Steady state Solution 2 • P2 = 7 bars • T2= 40 ºC • A2 = 25 cm2 • P3 = 7 bars • Sat. Liquid • A3V3=0.06m3/s FWH 3 Example: Feed Water Heater 1 • P1 = 7 bars • T1= 200 ºC • m1 = 40 kg/s Basic Equations**A direct contact feed-water heater is shown in the sketch.**Water at 7 bars and 40 C enters through a 25 cm2 port and is heated by steam entering at 7 bars and temperature of 200 C at a flow rate of 40 kg/s. The resulting saturated liquid leaves the FWH at 7 bars. Find: Mass flow rate at inlet 2 and exit 3. Assumptions: Steady state Solution 2 FWH 3 • P3 = 7 bars • Sat. Liquid • A3V3=0.06m3/s • P2 = 7 bars • T2= 40 ºC • A2 = 25 cm2 Example: Feed Water Heater 1 • P1 = 7 bars • T1= 200 ºC • m1 = 40 kg/s State 2 is defined. Find v2 and then design the volume flow rate and the area of the pipe.**Example: Aircraft Jet Engine Video**http://www.youtube.com/watch?v=ON0sVe1yeOk ME 200