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Units and Measurement
Question
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The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. if the speed of the liquid in the tube is v, the speed of the ejection of the liquid through the holes is

  • vR2/n2r2

  • vR2/nr2

  • vR2/n3r2

  • v2R/nr

Answer

B.

vR2/nr2

During the streamline of viscous and incompressible fluid through a pipe varying cross -section, the product of the area of cross section and normal fluid velocity (Av) remains constant throughout the flow.
Consider a cylindrical tube of a spray pump has radius R, one end having n fine holes, each of radius r and speed of liquid in the tube is v as shown in the figure.

According to equation of continuity
Av = constant
where A is a cylindrical tube and v is the velocity of the liquid in a tube. 
Volume in flow rate = volume an outflow rate
πR2v = nπr2v'
v' = R2v/nr2
Thus, speed of the ejection of the liquid through the holes is R2v/nr2

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