Question

The cylinderical tube of a spray pump has a cross-section of `8.0cm^(2)` one end of which has 40 fine holes each of diameter 1.0mm. If the liquid flow inside the tube is 1.5 m per minute, what is the speed of ejection of the liquid through the holes?

Answer 1

Area of corss-section of tube, `a_(1) = 8.0 cm^(2) = 8xx10^(-4)m^(2)`,
No. of holes = 40 , Diameter of each hole, `D= 1mm = 10^(-3)m`
`:.` radius of hole, `r=D/2 = 1/2 xx10^(3)m=5xx10^(-4)`
Area of cross-section of each hole = `pi r^(2) = pi(5xx10^(-4))^(2)m^(2)`
Total area of cross-section of 40 holes, `a_(2) = 40 xx pi(5xx10^(-4))^(2)m^(2)`
Speed of liquid inside the tube, `upsilon_(1) = 1.5 m//min = 1.5/60 ms^(-1)`
If `upsilon_(2)` is the velocity of ejection of the liquid through the hole, then `a_(1)upsilon_(1) =a_(2)upsilon_(2) or upsilon_(2) = a_(1)upsilon_(1)//a_(2)`
`:. upsilon_(2) = ((8xx10^(-4))xx1.5)/(60xx40xxpixx(5xx10^(-4))^(2)) = 0.637ms^(-1)`.