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Chapter 2: Problem 13

Dynamics - Pressure in a vessel. The pressure in a vessel is \(30 \mathrm{~N} \mathrm{~cm}^{-2}\). If the pressure is reduced by \(\frac{7}{100}\) of its original value, calculate (a) the decrease in pressure, (b) the resulting pressure in the vessel.

Short Answer

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Question: The pressure in a vessel is initially 30 N/cm². If the pressure is reduced by 7%, find (a) the decrease in pressure, and (b) the resulting pressure in the vessel. Answer: (a) The decrease in pressure is 21000 N/m². (b) The resulting pressure in the vessel is 279000 N/m².

Step by step solution

01

Calculate the decrease in pressure

To find the decrease in pressure, we need to calculate \(\frac{7}{100}\) of the original pressure. First, let's convert the given pressure from \(30 N\,cm^{-2}\) to a more widely-used unit, \(N\,m^{-2}\). There are \(100 cm\) in \(1 m\), so the conversion factor is \((100)^{2}\): $$30 \mathrm{\frac{N}{cm^2} \times \frac{(100 cm)^2}{(1 m)^2}} = 300000\,\frac{N}{m^2}.$$ Now, we find the decrease in pressure: $$\mathrm{Decrease\,in\,pressure} = \frac{7}{100} \times 300000\,\frac{N}{m^2} = 21000\,\frac{N}{m^2}.$$
02

Calculate the resulting pressure

To find the resulting pressure in the vessel, subtract the decrease in pressure calculated in Step 1 from the initial pressure: $$\mathrm{Resulting\,pressure} = 300000\,\frac{N}{m^2} - 21000\,\frac{N}{m^2} = 279000\,\frac{N}{m^2}.$$ Therefore, (a) the decrease in pressure is \(21000\,\frac{N}{m^2}\), and (b) the resulting pressure in the vessel is \(279000\,\frac{N}{m^2}\).

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Most popular questions from this chapter

Consider the fractions \(\frac{2}{3}, \frac{5}{6}\) and \(\frac{7}{8}\). (a) Calculate the l.c.m. of their denominators. (b) Express each fraction as an equivalent fraction with the l.c.m. found in (a) as the denominator.

Calculate the following, expressing your answer as an improper fraction: (a) \(1 \frac{2}{5}+2 \frac{3}{4}\) (b) \(4 \frac{1}{3}+6 \frac{3}{7}\) (c) \(2 \frac{4}{5}-1 \frac{2}{3}\) (d) \(6 \frac{1}{2}-3 \frac{3}{4}+2 \frac{1}{5}\) (e) \(3 \frac{1}{3}-4 \frac{4}{9}\)

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(a) Express \(\frac{3}{5}\) as an equivalent fraction with a denominator of 40 . (b) Express \(\frac{9}{30}\) as an equivalent fraction with a denominator of 10 . (c) Express 6 as an equivalent fraction with a denominator of 4 .

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