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Problem 4.119

# Problem 4.119 - Then V z V 2 2 g ⋅ z ⋅ = Also V π 4...

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Problem *4.119 [Difficulty: 3] Given: Water faucet flow Find: Expressions for stream speed and diameter; plot Solution: Basic equation: Bernoulli p ρ V 2 2 + g z + const = Assumptions: Laminar, frictionless, uniform flow The given data is D 0 5 mm = h 50 mm = Q 1 L 3 min = Q 0.333 L min = The initial velocity is V 0 Q π 4 D 0 2 = V 0 0.283 m s = Then applying Bernoulli between the exit and any other location p atm ρ V 0 2 2 + p atm ρ V 2 2 + g z = (z downwards) Then
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Unformatted text preview: Then V z ( ) V 2 2 g ⋅ z ⋅ + = Also V π 4 ⋅ D 2 ⋅ V π 4 ⋅ D 2 ⋅ = so D z ( ) D 1 2 g ⋅ z ⋅ V 2 + ⎛ ⎜ ⎝ ⎞ ⎠ 1 4 = Evaluating at h V h ( ) 1.03 m s = D h ( ) 2.62 mm ⋅ = 2.5 − 1.5 − 0.5 − 0.5 1.5 2.5 40 30 20 10 Diameter (mm) Height (mm) 10 20 30 40 50 0.25 0.5 0.75 1 1.25 z (mm) V (m/s)...
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