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The cylindrical tube of a spray pump has a cross-section of 8.0 cm2, one end of which has 40 line holes each of diameter 1.0 mm. If the liquid flows inside the tube is 1.5 m min-1. What is the speed of ejection of the liquid through the holes? |
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Answer» Here area of cylindrical tube a1 = 8.0 cm2 = 8 x 103 m2 Velocity of flow, v1 = 1.5 m min-1 = 1.5/60 ms-1 = 2.5 x 10-2 ms-1 Area of each hole = πD2/4 = {3.14 x (1 x 10-3)2}/{4} = 7.85 x 10-7 m2 Total area of all the 40 holes is, a2 = 40 x 7.85 x 10-7 m2 = 3.14 x 10-5 m2 If v2 is the velocity of ejection of liquid, then from the continuity equation, a1v1 = a2v2 ⇒ v2 = {a1v2}/{a2} = {8 x 10-4 x 2.5 x 10-2}/{3.14 x 10-5} = 0.637 ms-1 = 0.64 ms-1 |
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