Answer to Question #166204 in Physics for gibson mkandawire

Question #166204

1.Turpentine oil is flowing through a tube of length l and radius r. The pressure difference between the two ends of the tube is P. The viscosity of the oil is given by

πœ‚=𝑃(π‘Ÿ2βˆ’ π‘₯2)/4𝑣𝑙

Where v is the velocity of oil at a distance x from the axis of the tube. Determine the dimensions of Ξ·.

2. The position x of a particle depends upon time t according to the equation x = at + bt2. Determine the dimensions and units of a and b. What are the physical quantities denoted by a and b?

3. The velocity v of a particle depends upon time t according to the relation

𝑣=π‘Žπ‘‘+ 𝑏/𝑑+𝑐

What are the dimensions of a, b and c?



1
Expert's answer
2021-03-10T17:22:21-0500

1 We have:

[Ξ·]=P(r2βˆ’x2)4vl=Paβ‹…mm/sβ‹…m= =Pam/s=kgm2s=Nβ‹…s/m2.[\eta]=\frac{P(r_2-x_2)}{4vl}=\frac{\text{Pa}Β·\text{m}}{\text{m/s}\cdot\text{m}}=\\\space\\ =\frac{\text{Pa}}{\text{m/s}}=\frac{\text{kg}}{\text{m}^2\text{s}}=\text{N}Β·\text{s}/\text{m}^2.

2 The physical quantities denoted by a and b are initial velocity and acceleration: x is in meters, so


\text{m}=[a]Β·\text{s},\\ [a]=\text{m/s}.\\ \text{m}=[b]Β·\text{s}^2,\\ [b]=\text{m/s}^2.

3 Same approach as in (2):


\text{m/s}=[a]Β·\text{s},\\ [a]=\text{m/s}^2.\\ \text{m/s}=[b]/\text{s},\\ [b]=\text{m}.\\ \text{m/s}=[c].

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