JEE Main 2022 · 26 Jun · Shift 1 · Physics Q60

← JEE Main 2022 · 26 Jun · Shift 1

PhysicsInteger+4 / -1Question 60 of 90

An ideal fluid of density 800 kg m $^{-3}$ , flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from $a$ to $\dfrac a2$ . The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, the velocity of fluid is $\dfrac{\sqrt x}6$ ms $^{-1}$ for $x=$ ______. (Given $g=10$ ms $^{-2}$ )

A pipe bending downward: the wide end (area a, velocity v1) is at the upper left, h = 1 m above the narrow end (area a/2, velocity v2) at the lower right.

Your answer

Answer and worked solution

Official answer: 363

Continuity. $v_2=2v_1$ (area halves).

Bernoulli (wide end 1 m higher): $P_1-P_2=\frac12\rho(v_2^2-v_1^2)-\rho gh=1200v_1^2-8000=4100$ .

Speed. $v_1^2=\dfrac{12100}{1200}=\dfrac{121}{12}$ , so $v_1=\dfrac{11}{2\sqrt3}=\dfrac{\sqrt{363}}6$ : $x=363$ .

Answer: 363

Topics:Bernoulli's principle Continuity equation

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JEE Main 2022 · 26 Jun · Shift 1, Physics question 60