The gage pressure in a liquid at a depth of 3 m is read to...

namenerk

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

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 P1 is the gage pressure at depth of h1=3m and similarly we can define P2 as the gage pressure at depth of h2=9m.
Then we could obtain P1 and P2 as:
P1=ρL g h1 (1)
P2=ρL g h2 (2)
Dividing equ. (2) by equ. (1)
P2P1=ρLgh2ρLgh1
P2=P1h2h1
=42(kPa)93
=126kPa

encolatgehu

encolatgehu

Expert

2022-01-11Added 27 answers

Given,
Depth 1=h1=3m
Gage pressure at depth 1=Pg1=42kPa
Depth 2=h2=9m
Total pressure in liquid is given by,
P=Pa+ρgh
Where,
Pa= Atmoshpheric pressure
ρ= Density of liquid
g= Gravitational acceleration
h= depth
Gage pressure is given by,
Pg=PPa=ρgh
Step 2
Gage pressure at depth 1 is given by,
Pg1=ρgh1(eq.i)
Gage pressure at depth 2 is given by,
Pg2=ρgh2(eq.ii)
Taking ration of equaion (i) and (ii),
Pg1Pg2=ρgh1ρgh2
PgqPg2=h1h2
39
Pg2=42×93
Pg2=126kPa
Answer:
Gage pressure at depth of 9m=126kPa

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