The radius of the cross-section of the cylind | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given: Radius of the tube $r_1 = 2 \,cm = 0.02 \,m$.Radius of each hole $r_2 = 0.4 \,mm = 0.0004 \,m$.Number of holes $n = 50$.Speed of liquid ins

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) Given: Radius of the tube $r_1 = 2 \,cm = 0.02 \,m$.Radius of each hole $r_2 = 0.4 \,mm = 0.0004 \,m$.Number of holes $n = 50$.Speed of liquid inside the tube $v_1 = 0.04 \,ms^{-1}$.According to the equation of continuity, the volume flow rate inside the tube must equal the total volume flow rate through all the holes:$A_1 v_1 = n A_2 v_2$Substituting the areas $\pi r_1^2 v_1 = n \pi r_2^2 v_2$$r_1^2 v_1 = n r_2^2 v_2$$(0.02)^2 	imes 0.04 = 50 	imes (0.0004)^2 	imes v_2$$4 	imes 10^{-4} 	imes 0.04 = 50 	imes 16 	imes 10^{-8} 	imes v_2$$1.6 	imes 10^{-5} = 800 	imes 10^{-8} 	imes v_2$$1.6 	imes 10^{-5} = 8 	imes 10^{-6} 	imes v_2$$v_2 = \frac{1.6 	imes 10^{-5}}{8 	imes 10^{-6}} = 0.2 	imes 10 = 2 \,ms^{-1}$.

Similar Questions

The cylindrical tube of a spray pump has a cross-section of $8.0 \; cm^{2}$,one end of which has $40$ fine holes each of diameter $1.0 \; mm$. If the liquid flow speed inside the tube is $1.5 \; m \, min^{-1}$,what is the speed (in $m/s$) of ejection of the liquid through the holes?

Water flows through a horizontal pipe of variable cross-section at the rate of $12 \pi$ litre per minute. The velocity of the water at the point where the diameter of the pipe becomes $2 \text{ cm}$ is (in $\text{ m/s}$)

In the given figure,the velocity of the fluid $v = $ . . . . . . $m/s$.

$A$ horizontal tube of non-uniform cross-section has radii of $0.1 \,m$ and $0.05 \,m$ respectively at $M$ and $N$. For a streamline flow of an incompressible liquid, the rate of liquid flow is

Explain streamline and streamline flow.

Vedclass Test Series

Exam Paper Generator

Online Exam Module