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? | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-10 Mechanical Properties of Fluids



Q.16:- 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:-



Area of cross-section of the spray pump, A1 = 8 cm= 8 × 10–4 m2
Number of holes, n = 40
Diameter of each hole, d = 1 mm = 1 × 10–3 m
Radius of each hole, r = d/2 = 0.5 × 10–3 m
Area of cross-section of each hole, = πr= π (0.5 × 10–3)2 m2
Total area of 40 holes, An × a
= 40 × π (0.5 × 10–3)2 m2
= 31.41 × 10–6 m2
Speed of flow of liquid inside the tube, V= 1.5 m/min = 0.025 m/s
Speed of ejection of liquid through the holes = V2
According to the law of continuity, we have:
A1V1 = A2V2
V2 = A1V1 / A2
= 8 × 10-4 × 0.025 / (31.61 × 106)
= 0.633 m/s
Therefore, the speed of ejection of the liquid through the holes is 0.633 m/s.