Properties of Matter 3 Question 6

12. After the drop detaches, its surface energy is

(a) 1.4×106J

(b) 2.7×106J

(c) 5.4×106J

(d) 8.1×109J

Integer Answer Type Questions

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Answer:

Correct Answer: 12. 29025J/m3,29400J/m3

Solution:

  1. Given, A1=4×103m2,A2=8×103m2,

h1=2m,h2=5m,v1=1m/s and ρ=103kg/m3

From continuity equation, we have

A1v1=A2v2 or v2=(A1A2)v1 or v2=(4×1038×103)(1m/s)v2=12m/s

Applying Bernoulli’s equation at sections 1 and 2

p1+12ρv12+ρgh1=p2+12ρv22+ρgh2 or p1p2=ρg(h2h1)+12ρ(v22v12)

(a) Work done per unit volume by the pressure as the fluid flows from P to Q

W1=p1p2

=ρg(h2h1)+12ρ(v22v12)=(103)(9.8)(52)+12(103)(141)=[29400375]=29025J/m3

(b) Work done per unit volume by the gravity as the fluid flows from P to Q.

W2=ρg(h1h2)=(103)(9.8)(25) or W2=29400J/m3



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