Question

Water flowing through a 2.1-cm-diameter pipe can fill a 300 L bathtub in 4.4 min. What is the speed of the water in the pipe?

Answer 1

Given data :

Diameter of the pipe (d) = 2.1 cm = (2.1/100) m = 0.021m

Volume of the bathtub (V) = 300 L = (300/1000) m³ = 0.3 m³

^​​​​Time taken to fill the bathtub (t) = 4.4 min = (4.4 × 60) s = 264 s

Now,

Cross sectional area of the pipe (A) = πd²/4= (3.14 × 0.021²)/4

= 0.00034 m³

So, discharge (Q) = (V/t) = ( 0.3/264) = 0.0011 m³/s

So the speed of the water in the pipe is given by :

Q = v × A ( where v is the speed or velocity of the water)

$\therefore$ v = Q/A = (0.0011) /( 0.00034) = 3.23 m/s

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