To determine The power produced by the stream. Explanation Given: The diameter of the nozzle ( d ) is 50 mm . The cart moves to the right with a constant velocity V cs is 2 m / s The discharge from the nozzle ( Q ) is 0.04 m 3 / s . Calculations: Consider the flow as steady and the fluid can be taken as ideal. Figure 1 shows the free body diagram of the water stream striking. Consider the control volume as a portion of water striking the cart. Calculate the velocity V A at point A using the formula; V A = Q A A = Q ( π r 2 ) V A = 0.04 π ( 0.025 ) 2 = 20.37 m / s Here, Q is the flow rate of water and r is the radius of nozzle. Determine the relative velocity V A / c s of control surface at point A using the formula; V A / c s = V A − V c s V A / c s = 20.37 − 2 = 18.37 m/s Here, V c s is the velocity of cart. The relative velocity at point A , B , and C is equal to 18.37 m/s . V B / c s = V C / c s = V A / c s = 18.37 m / s Determine the relative flow Q A / c s at point A using the formula; Q A / c s = V A / c s A A = V A / c s ( π r 2 ) Q A / c s = 18.37 [ π ( 0.025 ) 2 ] = 0.03607 m 3 / s Determine the relative flow rate at point B using the formula; Q B / c s = 3 4 ( Q A / c s ) Q B / c s = 3 4 ( Q A / c s ) = 0.75 × ( 0.03607 ) = 0.02705 m 3 / s Determine the relative flow rate at point C using the formula; Q C / c s = 1 4 ( Q A / c s ) Q C / c s = 1 4 ( Q A / c s ) = 0.25 × ( 0.03607 ) = 0.009018 m 3 / s Express the linear momentum Equation as follows; ∑ F = ∂ ∂ t ∫ c v V ρ d V + ∫ c s V ρ V ⋅ d A Here, V is the velocity, ρ is the density of water, d V is the differential volume, and d A is the differential area

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ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 6, Problem 45P

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