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Water is flowing continuously from a tap having an internal diameter 8*10 -3 m. The water velocity as it leaves the tap is 0.4 ms -1 . The diameter of the water stream at a distance 2*10 -1 m below the tap is close to : (a) 7.5*10 -3 m (b) 9.6*10 -3 m (c) 3.6*10 -3 m (d) 5.4*10 -3 m

Water is flowing continuously from a tap having an internal diameter 8*10-3m. The water velocity as it leaves the tap is 0.4 ms-1. The diameter of the water stream at a distance 2*10-1m below the tap is close to :
(a) 7.5*10-3m
(b) 9.6*10-3m
(c) 3.6*10-3m
(d) 5.4*10-3m

Grade:11

2 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago

(c). From Bernoulli’s theorem,

P0 + 1/2 pv21pgh = p0 + 1/2 pv22 + 0

V2 = vv21 + 2gh = v0.16 + 2 * 10 *0.2 = 2.03 m/s

From equation of continuity

A2v2 = A1v1

pD22/4 * v2 = pD21/4v1

? D1D2 vv1/v2 = 3.55 * 10-3 m

ankit singh
askIITians Faculty 614 Points
2 years ago

Given data,

d1​=8×10−3m
v1​=0.4ms−1
h=0.2m
According to equation of motion,
v2​=v12​+2gh​
=(0.4)2+2×10×0.2​
≈2ms−1
∴ According to equation of continuity
 a1​v1​=a2​v2​
π×(28×10−3​)2×0.4=π×(2d2​​)2×2
d2​=3.6×10−3m

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