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  • 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 inside the tube is 1.5 m min^–1, what is the speed of ejection of the liquid through the holes ?

Q 10.16 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?

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Cross-sectional area of cylindrical tube is a1 = 8.0 cm2

The total area of the 40 fine holes is a2

\\a_{2}=40\pi (\frac{d^{2}}{4})\\ a_{2}=40\times \pi \times \frac{(10^{-3})^{2}}{4}\\ a_{2}=3.143\times 10^{-5}m^{2}

Speed of liquid inside the tube is v1 = 1.5 m min-1

Let the speed of ejection of fluid through the holes be v2

Using the continuity equation

\\a_{1}v_{1}=a_{2}v_{2}\\ v_{2}=\frac{a_{1}v_{1}}{a_{2}}\\ v_{2}=\frac{8\times 10^{-4}\times 1.5}{60\times 3.143\times 10^{-5}}\\ v_{2}=0.636\ m\ s^{-1}

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