Question

Find the applied pressure (in Pa) so that a square Si membrane of side 150 μm and thickness 5 μm deflects by 2 nm. Consider the Young’s Modulus of Si = 170 GPa.
Please send your answer with explanation guys.​

Answer 1

Explanation:

original volume of water , V = 1 L

Let change in volume of water is ∆V

A/C to question,

% change in volume of water = ∆V/V × 100

0.1 = ∆V/V × 100

∆V = 0.001

from data, bulk modulus of water,\betaβ = 2.2 × 10^9 N/m²

use formula, \beta=\frac{P}{\frac{\Delta{V}}{V}}β=

V

ΔV

P

so, P = \beta\left(\frac{\Delta{V}}{V}\right)β(

V

ΔV

)

P = 2.2 × 10^9 × 0.001

P = 2.2 × 10^6 N/m²

hence, the pressure on water should be 2.2 × 10^6 N/m²

Answer 2

Answer:

307.7 Pa

Explanation:

formulae applied

P= E h4/a4(4.54 Wo/h+2.33(Wo/h)3)

where

P => pressure

E => Young modules

h => thickness

Wo => deflection

a => sides