# What does the top pressure gauge in the figure read?

+1 vote
What does the top pressure gauge in the figure read?

by
selected by

Using Bernoulli's eqn.

P/ρg + v^2/2g + y = constant,

(P2 - P1)/ρg + [v2^2 - v1^2]/2g + (h2 - h1) = 0

=> (P2 - 200)/9.8ρ + [9 - 4]/19.6 + (3 - 2) = 0

=> P2 - 200 = - (1 + 5/19.6)*9.8ρ

=> P2 = 200 - 12.3ρ

To work out P, density ρ of the oil is needed without which answer cannot be worked out.

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat.
by

The solution is as follows...

p for oil = 900 kg/m^3

P2 = P1 + 1/2*p*(Vi^2 - Vf^2) + p*g*(y1 - y2)

The gauges include 1 atm, but because you would add the value to the initial gauge and subtract it from the final gauge, it's arbitrary...

P1 = 200 kPa P2 = ?

V1 = 2.0 m/s V2 = 3.0 m/s

y1 = 0 m y2 = 10 m

1 atm = 101,300 Pa (Its really 101,325 but Mastering Physics is dumb)

You'll want to convert everything to Pa as your p of 900 will mess things up if you don't..

P2 = 200,000 + (1/2 * 900) * (2^2 - 3^2) + (900 * 9.8) * (0 - 10)

= 200,000 + (450) * ( -5 ) + (8,820) * (-10)

= 200,000 + -2250 + -88,200

= 200,000 - 90,450

P2 = 109550 Pa (Answer in 3 sig-figs)

P2 = 110 kPa

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat.