General Physics> Find pressure at point A in the given fig...

Find pressure at point A in the given figure.........

Hasan Rizwi , 5 Years ago

Grade 12th pass

2 Answers

Samyak Jain

Last Activity: 5 Years ago

Let the adjacent point of sides l2 and l3 be B and that of sides l1 and l2 be D and the free surface of liquid at open end of pipe be E.Pressure at E = atmospheric pressure = Patm.Since fluid is static, pressure difference is due to height of fluid.Pressure at C = Pressure at E + \rhogh1,\rho = density of fluid in pipe and h1 = height of fluid between E and C = l1 sin\theta1.i.e. PC = Patm + \rhogl1 sin\theta1.Pressure at C = Pressure at B + \rhogh2 , h2 = l2 sin\theta2.i.e. PC = PB + \rhogl2 sin\theta2 \Rightarrow PB = PC – \rhogl2 sin\theta2 = Patm + \rhogl1 sin\theta1 – \rhogl2 sin\theta2Similarly, PA = PB + \rhogl3 sin\theta3 = Patm + \rhogl1 sin\theta1 – \rhogl2 sin\theta2 + \rhogl3 sin\theta3PA = \rhog(l1 sin\theta1 – l2 sin\theta2 + l3 sin\theta3) = pressure at A .

Samyak Jain

Last Activity: 5 Years ago

Let the adjacent point of sides l₂ and l₃ be B and that of sides l₁ and l₂ be C and the free surface of fluid

at open end of pipe be D.

Pressure at D = atmospheric pressure = P_atm.

Since fluid is static, pessure difference is due to height of fluid.

Pressure at C = Pressure at D + $\rho$ gh₁ .

$\rho$ = density of fluid in pipe and h₁ = height of fluid between E and C = l₁ sin $\theta$ ₁ .

P_C = P_atm + $\rho$ gl₁ sin $\theta$ ₁ .

Pressure at C = Pressure at B + $\rho$ gh₂ , h₂ = l₂ sin $\theta$ ₂ .

P_C = P_B + $\rho$ gl₂ sin $\theta$ ₂ $\Rightarrow$ P_B = P_C – $\rho$ gl₂ sin $\theta$ ₂ = P_atm + $\rho$ gl₁ sin $\theta$ ₁ – $\rho$ gl₂ sin $\theta$ ₂