© Laura Fellman, PCC Rock Creek Campus

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© Laura Fellman, PCC Rock Creek Campus Types of Fluid Flow Steady or laminar- Velocities are constant over time 2 m/s Unsteady (Turbulent) – Velocities not constant Compressible – Volume can change (most liquids are incompressible) Viscous – Thick, slow fluid © Laura Fellman, PCC Rock Creek Campus

In fluid dynamics, the continuity equation states that the rate at which mass enters a system is equal to the rate at which mass leaves the system plus any accumulation of mass within the system

mass of water per second = mass flow rate Av (kg/s) Consider a faucet: mass of water per second = mass flow rate Av (kg/s) Now consider a pipe that narrows: equal volumes L1 L2 Equation of Continuity If fluid is incompressible: (Av = volume flow rate) (m3/s) © Laura Fellman, PCC Rock Creek Campus

Continuity Equation examples: V1 V2 A stream of water gets narrower as it falls from a faucet (try it & see). Explain this phenomenon using the equation of continuity… When water falls

[1] A garden hose with cross-section area 12 cm2 is connected to a sprinkler cap consisting of 20 openings each of cross-section area 0.08 cm2. If the speed of the water in the hose was 2 m/s, then what is the speed of the water as it emerges from the holes in the sprinkler cap? The equation of continuity applies. Make sure to multiply the area of the sprinkler hole opening by 20 to get the total area. A1 v1 = A2 v2 (12 cm2)(2.0 m/s) = (20 x 0.08 cm2) v2 24 m/s = 1.6 v2 15 m/s = v2 [2] A stream of water emerges from a pipe. The cross-sectional area of the water stream at the tap is 1.2 cm2 and 43 mm lower than the tap is 0.35 cm2. At what volume rate of flow does the water flow from the tap? Ans: 3.21 x 10-5 m3/s or 3.36 x 10-5 m3/s - more info needed?