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Mechanical Properties Of Fluids

Question
CBSEENPH11018942

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, what is the speed of ejection of the liquid through the holes?

Solution

Area of cross-section of cylindrical tube, A = 8 cm

Velocity of flow in the tube, v = 1.5 m/min = 2.5 cm/sec 
Diameter of the hole, d = 1 mm = 0.1 cm 
Area of one hole, aoπd squared over 4 space equals space 2.5 space pi cross times 10 to the power of negative 3 end exponent space c m squared space
Total area of 40 holes, a = 40 a40 cross times 2.5 straight pi space cross times 10 to the power of negative 3 end exponent space cm squared space
= 0.1 straight pi space space cm squared
Let v' be the velocity of the ejection of the liquid through the holes. 
Using equation of continuity, 
AV = av
Putting the values, we get
straight v space equals space AV over straight a space equals space fraction numerator 8 cross times 2.5 over denominator 0.1 space straight pi end fraction space

space space space space space space space space space space space space space space space space space equals space 200 over straight pi
space space space space space space space space space space space space space space space space space equals space 64 space cm divided by sec