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Question: The cylindrical tube of a spray pumps has a cross-section of \(6 \mathrm {~cm} ^ { 2 }\) one of whic...

The cylindrical tube of a spray pumps has a cross-section of 6 cm26 \mathrm {~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 minute, then the speed of ejection of the liquid through the holes is

A

(a) 2.1 m s−12.1 \mathrm {~m} \mathrm {~s} ^ { - 1 }

A

(b) 0.31 m s−10.31 \mathrm {~m} \mathrm {~s} ^ { - 1 }

A

(c) 0.96 m s−10.96 \mathrm {~m} \mathrm {~s} ^ { - 1 }

A

(d) 3.4 m s−13.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }

Explanation

Solution

(b) Here, area of cross section of tube

Number of holes = 50

Diameter of each hole D = 1 mm =10−3 m= 10 ^ { - 3 } \mathrm {~m}

Radius of hole,

Area of cross section of each hole

=πr2=π(5×10−4)2 m2= \pi \mathrm { r } ^ { 2 } = \pi \left( 5 \times 10 ^ { - 4 } \right) ^ { 2 } \mathrm {~m} ^ { 2 }

Total area of cross section of 50 holes,

Speed of liquid inside the tube,

=1.260 m s−1=0.02 m s−1= \frac { 1.2 } { 60 } \mathrm {~m} \mathrm {~s} ^ { - 1 } = 0.02 \mathrm {~m} \mathrm {~s} ^ { - 1 }

Let the velocity of ejection of the liquid through the hole

As

Or