derive an equation related to pascal's law.
Answers
Answer:
We can calculate the value of force using Pascal's Law formula. ... A piston of small cross-section A is used to exert a force F directly on the liquid. The pressure P =F/A is transmitted throughout the liquid to the larger cylinder attached with a larger piston of area B, which results in an upward force of P × B.
The formula for Pascal’s Law
The following is the formula for Pascal’s law:
F = PA
where,
- F be the force applied
- P be the pressure transmitted
- A be the cross-sectional area
Derivation of Pascal’s Law
Consider an arbitrary right-angled triangle in a liquid of density rho (ρ). Since the element is very small, each point is assumed to be at the same depth from the liquid surface. The effect of gravity is the same at all these points.
( see the above triangle diagram)
Let, ab, bd and cd is the cross-sectional area of the faces ABFE, ABDC, and CDFE respectively.
Let, P1, P2, and P3 is the pressure transmitted on the faces ABFE, ABDC, and CDFE.
The pressure exerts a force that is normal to the surface. Let, P1 exert force F1 on the surface ABFE, P2 exert force F2 on the surface ABDC, and P3 exert force F3 on the surface CDFE respectively.
Therefore,
F1 = P1 × area of ABFE = P1 ad
F2 = P2 × area of ABDC = P2 bd
And, F3 = P3 × area of CDFE = P3 cd
Also,
The prism net force will be zero because the prism is in equilibrium.
F1 sin θ = F2
F1 cos θ = F3
pressure,
P1 ad ba = P2 bd (equation-i)
P1 ad ca = P3 cd (equation-ii)
From (i) and (ii),
P1 = P2 and P1 = P3
∴ P1 = P2 = P3
hopefully its helped u dear :)
