Problem 1.53

# Problem 1.53 - Problem 1.53[Difficulty 5 V = 0.001 in D =...

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Problem 1.53 [Difficulty: 5] Given: Syringe pump to deliver 100 mL/min δ V 0.001 in min = δ D 0.0005 in = Find: (a) Plot uncertainty in flow rate as a function of bore. (b) Find combination of piston speed and bore resulting in minimum uncertainty in flow rate. Solution: We will apply uncertainty concepts. Governing Equations: Q π 4 D 2 V = (Flow rate in syringe pump) 2 1 2 1 1 1 + ± = L x R u x R R x u (Propagation of Uncertainties) Now solving for the piston speed in terms of the bore: VD () 4Q π D 2 = 2 1 2 2 2 1 2 2 2 + ± = + ± = V D V D Q u V Q Q V u D Q Q D u V Q Q V u D Q Q D u So the uncertainty in the flow rate is: () ( ) [] 2 1 2 2 2 V D Q u u u + ± = 0 = D u Q where u D δ D D =

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Problem 1.53 - Problem 1.53[Difficulty 5 V = 0.001 in D =...

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