Fluid flow – Important Formulas (for class 11)

Last updated on June 24th, 2023 at 01:40 pm

This post presents a list of facts and formulas from the Fluid flow chapter of class 11 (grade 11) physics.

Formulas from the Fluid Flow chapter of class 11

1 ) Pressure is the force per unit area exerted by a fluid on its surroundings:
P = F/A

Its SI units are pascals where 1 pascal = 1 newton/meter squared.

Pressure is also measured in “atmospheres” (the pressure of air at or near sea level) where 1 atmosphere ≈ 10⁵ pascals.

2 ) The pressure in an incompressible fluid varies with depth according to:
P = P₀ + ρgD

where P₀ is the pressure at the top and D is the depth.

3 ) Pascal’s Principle – Pressure applied to a fluid is transmitted undiminished to all points of the fluid.

4 ) Archimedes’ Principle – The buoyant force on an object F_b = ρgV_disp
where V_disp is the volume of fluid displaced by an object.

5 ) Conservation of Flow – for steady/laminar flow in the absence of turbulence and viscosity.
I = A₁v₁ = A₂v₂
where I is the flow, the volume per unit time that passes a given point in e.g. a pipe. This equation is also known as the continuity equation.

6 ) Consider the flow of fluid in a closed pipe that can e.g. go up and down, the work-mechanical energy theorem per unit volume of the fluid can be written as Bernoulli’s Equation: P +(1/2)ρv² + ρgh = constant

7 ) Venturi Effect – At the constant height, the pressure in a fluid decreases as the velocity of the fluid increases (the work done by the pressure difference is what speeds up the fluid!. This is responsible for e.g. the lift of an airplane wing and the force that makes a spinning baseball or golf ball curve.

8) Torricelli’s Rule: If a fluid is flowing through a very small hole (for example at the bottom of a large tank) then the velocity of the fluid at the large end can be neglected in Bernoulli’s Equation.

In that case, the exit speed is the same as the speed of a mass dropped the same distance:
v =(2gH)^1/2 where H is the depth of the hole relative to the top surface of the fluid in the tank.