Water flows through a horizontal pipe that narrows from cross-section A₁ = 8 cm² to A₂ = 2 cm² — JEE Physics
Water flows through a horizontal pipe that narrows from cross-section $A_1 = 8\ cm^2$ to $A_2 = 2\ cm^2$. If the velocity at the wider section is $v_1 = 1$ m/s, find $v_2$ and the pressure difference.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
▲ 16
By continuity: $A_1 v_1 = A_2 v_2$
$$v_2 = \frac{A_1 v_1}{A_2} = \frac{8 \times 1}{2} = 4 m/s$$
By Bernoulli: $P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2$
$$\Delta P = P_1 - P_2 = \frac{1}{2}\rho(v_2^2 - v_1^2) = \frac{1}{2}\times1000\times(16-1)$$
$$\Delta P = 7500 Pa$$
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Discussion (4)
RV
Tip for others: you can verify the answer quickly by checking the units.
R
Brilliant explanation, the substitution step is what I kept missing.
N
What changes if the medium/conditions were different?
VA
Great discussion here. If you want more practice on this concept, check the related questions in this category.