The volume of liquid flowing per second is called the volume flow rate Q and has the dimensions of [L][T]. The flow rate of a liquid through a hypodermic needle during an injection can be estimated 60. with the following equation: TR"(P2 – P,) 8nL The length and radius of the needle are L and R, respectively, both of which have the dimension [L]. The pressures at opposite ends of the nee- dle are P, and P,, both of which have the dimensions of [M]/{[L][T]*}. The symbol 7 represents the viscosity of the liquid and has the dimen- sions of [M]/{[L][T]}. The symbol 7 stands for pi and, like the number 8 and the exponent n, has no dimensions. Using dimensional analysis, de- lermine the value of n in the expression for Q.

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The volume of liquid flowing per second is called the volume
flow rate Q and has the dimensions of [L][T]. The flow rate of a
liquid through a hypodermic needle during an injection can be estimated
60.
with the following equation:
TR"(P2 – P,)
8nL
The length and radius of the needle are L and R, respectively, both of
which have the dimension [L]. The pressures at opposite ends of the nee-
dle are P, and P,, both of which have the dimensions of [M]/{[L][T]*}.
The symbol 7 represents the viscosity of the liquid and has the dimen-
sions of [M]/{[L][T]}. The symbol 7 stands for pi and, like the number 8
and the exponent n, has no dimensions. Using dimensional analysis, de-
lermine the value of n in the expression for Q.
Transcribed Image Text:The volume of liquid flowing per second is called the volume flow rate Q and has the dimensions of [L][T]. The flow rate of a liquid through a hypodermic needle during an injection can be estimated 60. with the following equation: TR"(P2 – P,) 8nL The length and radius of the needle are L and R, respectively, both of which have the dimension [L]. The pressures at opposite ends of the nee- dle are P, and P,, both of which have the dimensions of [M]/{[L][T]*}. The symbol 7 represents the viscosity of the liquid and has the dimen- sions of [M]/{[L][T]}. The symbol 7 stands for pi and, like the number 8 and the exponent n, has no dimensions. Using dimensional analysis, de- lermine the value of n in the expression for Q.
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