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3 years ago

6

Motor oil, with a viscosity of 0.25 N ∙ s/m 2, is flowing through a tube that has a radius of 5.0 mm and is 25 cm long. The drop

in pressure is 300 kPa. What is the volume of oil flowing through the tube per second?

1 answer:

Sergio039 [100]3 years ago

7 0

Answer:

1.18 x 10^-3 m^3/s

Explanation:

η = 0.25 N s/m^2, radius, r = 5 mm = 0.005 m, l = 25 cm = 0.25 m

P = 300 kPa = 300,000 Pa, Volume of flow = ?

By use of Poiseuillie's equation

Volume of flow = π P r^4 / (8 η l)

Volume of flow = (3.14 x 300000 x 0.005^4) / (8 x 0.25 x 0.25)

Volume of flow = 1.18 x 10^-3 m^3/s

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Answer:

Approximately $\rm 5.7\; \mu F$ and approximately $29\; \rm \mu F$ .

Explanation:

Let $C_1$ and $C_2$ denote the capacitance of these two capacitors.

When these two capacitors are connected in parallel, the combined capacitance will be the sum of $C_1$ and $C_2$ . (Think about how connecting these two capacitors in parallel is like adding to the total area of the capacitor plates. That would allow a greater amount of charge to be stored.)

$C(\text{parallel}) = C_1 + C_2$ .

On the other hand, when these two capacitors are connected in series, the combined capacitance should satisfy:

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(Consider how connecting these two capacitors in series is similar to increasing the distance between the capacitor plates. The strength of the electric field ( $V$ ) between these plates will become smaller. That translates to a smaller capacitance if the amount of charge stored $(Q)$ stays the same.)

The question states that:

$C(\text{parallel}) = 35\; \rm \mu F$ , and
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Let the capacitance of these two capacitors be $x\; \rm \mu F$ and $y\; \rm \mu F$ . The two equations will become:

$\displaystyle \left\lbrace \begin{aligned}& x + y = 35 \\ & \frac{1}{x} + \frac{1}{y} = \frac{1}{4.8}\end{aligned}\right.$ .

From the first equation:

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$\displaystyle \frac{1}{x} + \frac{1}{35 - x} = \frac{1}{4.8}$ .

Solve for $x$ :

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Substitute back into the equation $y = 35 - x$ for $y$ :

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In other words, these two capacitors have only one possible set of capacitances (even though the previous quadratic equation gave two distinct real roots.) The capacitances of the two capacitors would be approximately $5.7\; \rm \mu F$ and approximately $29\; \rm \mu F$ (both values are rounded to two significant digits.)

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