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Standard IX

Physics

Centripetal Force

An incompress...

Question

An incompressible non-viscous fluid (density $δ$ ) flows steadily through a cylindrical pipe which has radius $2$ R at point A and radius R at point B(at the same height as A) further along the flow direction. If the velocity and pressure at point A are v and P, respectively, find the pressure at B.

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Solution

By equation of continuity
$A_{1} v_{1} = A_{2} v_{2}$
$π 4 R^{2} v = π R^{2} v_{2}$
$v_{2} = 4 v$
by bernoulli's equation $△ P = \frac{1}{2} ϱ (v_{2}^{2} - v_{1}^{2})$
$P_{B} - P_{A} = \frac{15}{2} ϱ v^{2}$
$P_{B} = P + \frac{15}{2} ϱ v^{2}$

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An incompressible non-viscous fluid (density δ) flows steadily through a cylindrical pipe which has radius 2R at point A and radius R at point B(at the same height as A) further along the flow direction. If the velocity and pressure at point A are v and P, respectively, find the pressure at B.

By equation of continuity A1v1=A2v2 π4R2v=πR2v2 v2=4vby bernoulli's equation △P=12ϱ(v22−v21) PB−PA=152ϱv2 PB=P+152ϱv2

By equation of continuity
$A_{1} v_{1} = A_{2} v_{2}$
$π 4 R^{2} v = π R^{2} v_{2}$
$v_{2} = 4 v$
by bernoulli's equation $△ P = \frac{1}{2} ϱ (v_{2}^{2} - v_{1}^{2})$
$P_{B} - P_{A} = \frac{15}{2} ϱ v^{2}$
$P_{B} = P + \frac{15}{2} ϱ v^{2}$