Presentation on theme: "Conservation laws • Laws of conservation of mass, energy, and momentum. • Conservation laws are first applied to a fixed quantity of matter called a closed."— Presentation transcript:
1Conservation laws• Laws of conservation of mass, energy, and momentum.• Conservation laws are first applied to a fixed quantity ofmatter called a closed system or just a system, andthen extended to regions in space called controlvolumes.• The conservation relations are also called balanceequations since any conserved quantity must balanceduring a process.
2Continuity Equation Conservation of mass for a system Time rate of change of the system mass =0For a system and a fixed nondeforming control volume that are coincident at an instant of time ,with B - mass and b=1 we see atFigure 5.1 (p. 194)System and control volume at three different instances of time. (a) System and control volume at time t – δt. (b) System and control volume at time t, coincident condition. (c) System and control volume at time t + δt.
3• Time rate of change of the mass of the system = time rate of change in the mass of the control volume + net rate of flow of mass through control surface.• Time rate of change in the mass of the control volume =• Net rate of flow of mass through control surface =• For steady flow,• Net mass flow rate through the control surface =where m mass flow rate( slug/s;kg /s)
4Continuity Equation• Conservation of mass: for a fixed, non deforming control volume• More commonly used:• Average velocity:
6Example 1• Seawater flows steadily through a simple conical-shaped nozzle. If the nozzle exit velocity =20 m/s, determine the minimum pumping capacity in m3/s.
7Example 2• Airflows steadily between two sections in a long straight portion of 4-in diameter pipe. The uniformly distributed temperature and pressure at each section are given. If the average air velocity at section (2) is 100 ft/s, calculate the average air velocity at section (1).
8Example 3Moist air enters a dehumidifier at the rate of 22 slugs/hr. Determine the mass flow rate of the dry air and the water vapor leaving the dehumidifier.
9Example 4A bathtub is being filled with water from a faucet. The rate of flow from the faucet is steady at 9 gal/min. The tub volume is approximated by a rectangular space.
11Moving, Non deforming Control Volume V = W +VCVV= absolute velocity, VW= relative velocity of fluid seen by an observer moving with the control volume velocity, VcvContinuity equation for a moving non-deforming control volume
12Example 5. An airplane moves forward at a speed of 971 km/hr Example 5. An airplane moves forward at a speed of 971 km/hr. The frontal intake area of the jet engine is 0.80 m2, and the entering air density is kg/m3. A stationary observer determines that relative to the earth, the jet engine exhaust gases moves away from the engine with a speed of 1050 km/hr. The engine exhaust area is m2, and the exhaust gas density is kg/m3. Estimate the mass flow arte of fuel into the engine in kg/hr.