Question

Small droplets of carbon tetrachloride at 68 °F are formed with a spray nozzle. If the average diameter of the droplets is 200 um, what is the difference in pressure between the inside and outside of the droplets?

Answer 1

Answer:

the difference in pressure between the inside and outside of the droplets is 538 Pa

Explanation:

given data

temperature = 68 °F

average diameter = 200 µm

to find out

what is the difference in pressure between the inside and outside of the droplets

solution

we know here surface tension of carbon tetra chloride at 68 °F is get from table 1.6 physical properties of liquid that is

σ = 2.69 × $10^{-2}$ N/m

so average radius = $\frac{diameter}{2}$ =  100 µm = 100 ×$10^{-6}$ m

now here we know relation between pressure difference and surface tension

so we can derive difference pressure as

2π×σ×r = Δp×π×r²    .....................1

here r is radius and  Δp pressure difference and σ surface tension

Δp = $\frac{2 \sigma }{r}$    

put here value

Δp = $\frac{2*2.69*10^{-2}}{100*10^{-6}}$  

Δp = 538

so the difference in pressure between the inside and outside of the droplets is 538 Pa