Application of the Continuity Equation Dr. Eyad Abushandi.

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Presentation transcript:

Application of the Continuity Equation Dr. Eyad Abushandi

2 Example No. 4 A 10 cm jet of water issues from a 1 m diameter tank. Assume that the velocity in the jet is m/s where h is the elevation of the water surface above the outlet jet. How long will it take for the water surface in the tank to drop from h 0 = 2 m to h f = 0.50 m?

3 Example No. 4 Situation: Water draining by a 10 cm jet from 1 m diameter tank. Find: Time (in seconds) to drain from depth of 2 m to 0.5 m. Plan 1. Apply the continuity equation. 2. Analyze term by term. 3. Solve the equation for elapsed time. 4. Calculate time to change levels.

4 Example No. 4 Solution: Continuity equation

5 Example No. 4 Solution: Accumulation rate term where A T is cross-sectional area of tank. Inlet mass flow rate with no inflow is:

6 Example No. 4 Solution: · Outlet mass flow rate Substitution of terms in continuity equation:

7 Example No. 4 Solution: Equation for elapsed time: Separating variables Or

8 Example No. 4 Solution: Integrating Substituting in initial condition, h(0) = h 0, and final condition, h(t) = h f, and solving for time

9 Example No. 4 Solution: Time calculation: Evaluating tank and outlet areas

10 Example No. 4 Solution: Elapsed time