In streamline flow, water entering a pipe having diameter of 2 cm and the speed of water is 1 m per second. Eventually, the pipe tapers to a diameter of 1 cm. Calculate the speed of water where diameter of pipe is 1 cm.
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the discharge from section 1 to section per unit till will be same,if the flow is streamline that means A1V1=A2V2 ,area 1* velocity at 1 = area 2* velocity at 2.put the values in equation,you will get the velocity at 2.
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The speed of water is 4 m/s
If the cross section of pipe is A and the velocity is v, then,
Av = constant
⇒ d²v = constant [∵ A = πd²/4, d= diameter of the area of cross section]
The diameter of the pipe where the water is entering is = 2 cm = 0.02 m
The velocity of water at this point is = 1 m/s
The pipe tapers to a diameter of 1 cm = 0.01 m
Suppose, the velocity of water at this point = v
∴ 0.02² × 1 = 0.01² × v
⇒ v = 4
∴ The velocity of water is 4 m/s.
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