The cylindrical tube of a spray pump has a cross-sectional area of $10 \mathrm{~cm}^2$. One end has

Question

The cylindrical tube of a spray pump has a cross-sectional area of $10 \mathrm{~cm}^2$. One end has 20 fine holes, each of cross-sectional area $0.1 \mathrm{~cm}^2$. If the speed of the liquid inside the main tube is $1.5 \mathrm{~m/s}$, the speed of the ejection of the liquid through the holes is

Professor PC Thomas Classes · Answer

(c) : According to the principle of continuity, the volume flow rate must be constant. The total flow rate in the main tube is $A 	imes V = 10 \mathrm{~cm}^2 	imes 1.5 \mathrm{~m/s}$. The liquid is ejected from $n=20$ holes, so the total area of ejection is $n 	imes a = 20 	imes 0.1 \mathrm{~cm}^2 = 2 \mathrm{~cm}^2$. Let the ejection velocity be $v$. Then $A 	imes V = (n 	imes a) 	imes v \implies 10 	imes 1.5 = 2 	imes v \implies 15 = 2v$. Therefore, $v = 7.5 \mathrm{~m/s}$.