Schematic cross sectional view of baraj gate is shown in the figure. Find value of ( ℓ h ) 2 such that water is not allowed to flow?

Torque about the bottom edge from wall pressure: τ w a ll = ∫ 0 h ρ g ( h − y ) b d y ⋅ y = 6 ρ g b h 3 Torque from base pressure: τ ba se = ( ρ g h ) ( ℓ b ) 2 h No flow condition: τ ba se = τ w a ll 2 ρ g h 2 ℓ b = 6 ρ g b h 3 ⇒ ( ℓ h ) 2 = 3

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Physics - Fluid Question with Solution | TestHub

PhysicsFluidPressureMedium2 minQB

PhysicsMediuminteger

Schematic cross sectional view of baraj gate is shown in the figure. Find value of $(\frac{h}{ℓ})^{2}$ such that water is not allowed to flow?

Answer:

Solution:

Torque about the bottom edge from wall pressure: $τ_{w a ll} = \int_{0}^{h} ρ g (h - y) b d y \cdot y = \frac{ρ g b h ^{3}}{6}$

Torque from base pressure: $τ_{ba se} = (ρ g h) (ℓ b) \frac{h}{2}$

No flow condition: $τ_{ba se} = τ_{w a ll}$

$\frac{ρ g h ^{2} ℓ b}{2} = \frac{ρ g b h ^{3}}{6} \Rightarrow (\frac{h}{ℓ})^{2} = 3$

Stream:JEESubject:PhysicsTopic:FluidSubtopic:Pressure

⏱ 2mℹ️ Source: QB

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