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The CGS unit for measuring the viscosity of a liquid is the poise [P]: 1 P = 1 g/(s·cm). The SI unit is the kg/(s·m). The viscosity of water at 5°C is 2.06 ✕ 10-3 kg/(s·m). Express this viscosity in poise.

Respuesta :

Answer:

[tex]\mu = 2.06 \times 10^{-2}  P[/tex]

Explanation:

We have that [tex]1\, P = 1 \, \frac{g}{s\,cm}[/tex]

if the viscosity of water at 5°C is:

[tex]\mu = 2.06 \times 10^{-3} \frac{kg}{s\cdot m}[/tex]

To express this quantity in poise, we have to go from SI units to CGS units, we can do that by replacing kilograms by grams and meters by centimeters.

we know that:

[tex]1\, kg = 1000\, g\\\\1\,m = 100 \, cm[/tex]

Inserting this into the preceding equation we have:

[tex]\mu = 2.06 \times 10^{-3} \frac{kg}{s\cdot m}= 2.06 \times 10^{-3} \frac{1000}{100} \frac{g}{s\cdot cm}\\\mu = 2.06 \times 10^{-2} \frac{g}{s\cdot cm} = 2.06 \times 10^{-2} P\\\mu = 2.06\,c P[/tex]

Where [tex]cP[/tex] or centipoise is a hundredth of a poise