namenerk

Answered

2022-01-09

The gage pressure in a liquid at a depth of 3 m is read to be 42 kPa. Determine the gage pressure in the same liquid at a depth of 9 m.

Answer & Explanation

Donald Cheek

Expert

2022-01-10Added 41 answers

Given that the gage pressure at depth of 3 m is 42 kPa. To determine the gage pressure at depth 9 m we can consider that the pressure of the first case

Then we could obtain

Dividing equ. (2) by equ. (1)

encolatgehu

Expert

2022-01-11Added 27 answers

Given,

Depth$1={h}_{1}=3m$

Gage pressure at depth$1={P}_{g1}=42kPa$

Depth$2={h}_{2}=9m$

Total pressure in liquid is given by,

$P={P}_{a}+\rho gh$

Where,

${P}_{a}=$ Atmoshpheric pressure

$\rho =$ Density of liquid

$g=$ Gravitational acceleration

$h=$ depth

Gage pressure is given by,

${P}_{g}=P-{P}_{a}=\rho gh$

Step 2

Gage pressure at depth 1 is given by,

${P}_{g1}=\rho g{h}_{1}(eq.i)$

Gage pressure at depth 2 is given by,

${P}_{g2}=\rho g{h}_{2}(eq.ii)$

Taking ration of equaion (i) and (ii),

$\therefore \frac{{P}_{g1}}{{P}_{g2}}=\frac{\rho g{h}_{1}}{\rho g{h}_{2}}$

$\therefore \frac{{P}_{gq}}{{P}_{g2}}=\frac{{h}_{1}}{{h}_{2}}$

$\therefore \frac{3}{9}$

$\therefore {P}_{g2}=42\times \frac{9}{3}$

$\therefore {P}_{g2}=126kPa$

Answer:

Gage pressure at depth of$9m=126kPa$

Depth

Gage pressure at depth

Depth

Total pressure in liquid is given by,

Where,

Gage pressure is given by,

Step 2

Gage pressure at depth 1 is given by,

Gage pressure at depth 2 is given by,

Taking ration of equaion (i) and (ii),

Answer:

Gage pressure at depth of

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