Problem 5.51 - Problem 5.51 Given[Difficulty 2 Sediment...

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Problem 5.51 [Difficulty: 2] Given: Sediment concentration fates in a river after a rainfall are: t c 100 ppm hr x c 50 ppm mi Stream speed is 0.5 mph, where a boat is used to survey the concentration. The boat speed is 2.5 mph. Find: Physically the observed rates of change differ because the observer is convected through the flow. The convective change may add to or subtract from the local rate of change. Solution: We will apply the concept of substantial derivative t c z c w y c v x c u Dt Dc Governing Equation: (Substantial Derivative) Assumptions: (1) One-dimensional motion (velocity not a function of y or z) (2) Steady flow (velocity is not a function of t) t c x c u Dt Dc Based on the above assumptions, the substantial derivative reduces to: To obtain the rates of change from the boat, we set
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