The cylinderical tube of a spray pump has a cross-section of 6 cm^(2) one of which has 50 holes each of diameter 1 mm. If the liquid flow inside the tube is 1.2 m per minutes, then the speed of ejection of the liquid through the holes is

The cylinderical tube of a spray pump has a cross-section of 6 cm^(2)

1.	The cylinderical tube of a spray pump has a cross-section of 6 cm^(2) one of which has 50 holes each of diameter 1 mm. If the liquid flow inside the tube is 1.2 m per minutes, then the speed of ejection of the liquid through the holes is
Answer» 1. `2.1 m s^(-1)` `0.31 ms^(-1)` `0.96 m s^(-1)` `3.4 m s^(-1)` Solution :Here, area of cross section of tube `a_(1)=6 cm^(2)=6xx10^(-4) m^(2)` Number of holes =50 Diameter of each hole, D=1mm, `10^(-3)`m Radius of hole, `r=(D)/(2)=(1)/(2)xx10^(-3)=5xx10^(-4)`m Area of cross-section of each hole `=PIR^(2)=pi(5xx10^(-4))^(2) m^(2)` Speed of liquid inside the tube, `v_(1)=1.2 m "MIN"^(-1)=(1.2)/(60) m s^(-1)=0.02 m s^(-1)` Let the velocity of ejection of the liquid through the hole `v_(2)` As `a_(1)v_(1)=a_(2)v_(2)` or `v_(2)=(a_(1)v_(1))/(a_(2))=(6xx10^(-4)xx0.02)/(50xxpi(5xx10^(-4))^(2))=0.31 m s^(-1)`