Question

The cylindrical tube of a spray pump has a cross-section of 8.0 cm2 one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is 1.5 m min¯¹, what is the speed of ejection of the liquid through the holes ?

Answer 1

Given, the area of cross-section of the tube is 8.0  cm 2 . The number of holes is 40. The diameter of each hole is 1.0 mm and the flow rate of the liquid is 1.5 m/ min .

The total area of all 40 holes is given by the equation,

A 2 =40×( π 4 d 2 )

Substituting the value in the above equation, we get:

A 2 =40×( π 4 ( 1.0× 10 −3  m ) 2 ) =3.142× 10 −5   m 2

Let A 1 be the area of the cross-section of tube.

The continuity equation is,

A 1 v 1 = A 2 v 2

Substituting the values in the above equation, we get:

( 8.0× 10 −4   m 2 )( 1.5 m/ min × 1 min 60 s )=( 3.142× 10 −5   m 2 ) v 2 v 2 =0.64 m/s

Hence, the speed of ejection of liquid through the holes is 0.64 m/s .