Respuesta :
This problem requires our calculation to undergo the dimensional analysis approach. In this approach, you disregard the actual quantity and focus on the units of measurement. This helps us know the units of our final answer.
First, let's ignore 16. Let's focus on converting the units kPa-mm³/s to mJ/s. The unit kPa stands for kiloPascals which is 1000 times greater than 1 Pa. The unit mJ, on the other hand, stands for millijoules, which is 1000 times lesser than Joules. The relationship between the two is that, Joules = Pa × m³. But since we want our final answer to be mJ, that would be equal to Pa×mm³. Since the original unit already contains mm³, all we have to do is convert kPa to Pa.
16 kPa-mm³/s * (1000 Pa/1 kPa) = 16,000 Pa-mm³/s
Since Pa-mm³ is equal to mJ, the final conversion yields to 16,000 Pa-mm³/s.
First, let's ignore 16. Let's focus on converting the units kPa-mm³/s to mJ/s. The unit kPa stands for kiloPascals which is 1000 times greater than 1 Pa. The unit mJ, on the other hand, stands for millijoules, which is 1000 times lesser than Joules. The relationship between the two is that, Joules = Pa × m³. But since we want our final answer to be mJ, that would be equal to Pa×mm³. Since the original unit already contains mm³, all we have to do is convert kPa to Pa.
16 kPa-mm³/s * (1000 Pa/1 kPa) = 16,000 Pa-mm³/s
Since Pa-mm³ is equal to mJ, the final conversion yields to 16,000 Pa-mm³/s.
Answer:
[tex]Z = 16.0\ kPa\ mm^3\ s^{-1} = 16.0\times 10^{-3}\ mJ.s^{-1}[/tex]
Explanation:
Unit conversion is the multi-step process which involves the multiplication or the division by a specified numerical factor as well as the selection of the correct number of the significant digits and rounding.
There are various units in which physical parameters are expressed. In the given question qunatity is given in [tex] kPa\ mm^3\ s^{-1} [/tex] which has to be converted to [tex]mJ.s^{-1}[/tex].
Further Explanation:
The given unit conversion includes two steps:
Step 1
Conversion from [tex]kPa.mm^3.s^{-1}[/tex] to [tex]Pa.m^3.s^{-1}[/tex]
1kPa = [tex]10^3\ Pa[/tex]
[tex]1\ mm^3=10^{-9} m^3[/tex]
[tex]Z = 16.0\ kPa\ mm^3\ s^{-1}[/tex]
[tex]= 16.0\times (kPa\times \frac{10^3\ Pa}{1\ kPa} )\time (mm^3 \times \frac{10^{-9}\ m^3}{1\ mm^3} ).s^{-1}[/tex]
[tex]=16.0\times 10^{-6} Pa.m^3.s^{-1}[/tex]
Step 2
Convesion from [tex]=16.0\times 10^{-6} Pa.m^3.s^{-1}[/tex] to [tex] J.s^{-1}[/tex]
[tex]1\ Pa=1 \frac{N}{m^2}[/tex]
1 N.m = 1 J
[tex]=16.0\times 10^{-6} Pa.m^3.s^{-1} = 16.0 \times \frac{N}{m^2} .m^3 .s^{-1}
[tex]=16.0\times 10^{-6}\ J.s^{-1}[/tex]
[tex]1\ J = 10^{3}\ mJ[/tex]
[tex]16.0\times 10^{-6}\ J.s^{-1}=16.0\times (J\times \frac{10^3\ mJ}{1\ J}).s^{-1}[/tex]
[tex]=16.0\times 10^{-3}\ mJ.s^{-1}[/tex]
Learn More:
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Keywords:
Unit conversion, kPa, Pa, J,
