Question

Given: rho water ​

=1000( m 3
kg
​
) rho oil ​
=850( m 3
kg
​
) rho Mercury ​
=13,600( m 3
kg
​
) g=9.81( s 2
m
​
) h 1
​
=0.16 m
​
h 2
​
=0.31 m h 3
​
=0.49m Determine: P 1
​
, gage = ?? ( kPa
​
) Hint: P gage ​
=P 1
​
−P atm ​

Answer 1

Main answer:

P1, gage = 13.13 kPa

Step-by-step explanation:

To determine the gage pressure at point 1 (P1, gage), we can use the equation Pgage = P1 - Patm, where P1 is the absolute pressure at point 1 and Patm is the atmospheric pressure. We need to calculate P1 first and then subtract the atmospheric pressure.

Given the heights h1 = 0.16 m, h2 = 0.31 m, and h3 = 0.49 m, we can calculate the pressures at these points using the hydrostatic pressure equation P = ρgh, where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.

First, let's calculate the pressure at point 3 (P3). Using the density of mercury (ρMercury = 13,600 kg/m^3), the acceleration due to gravity (g = 9.81 m/s^2), and the height h3 = 0.49 m, we find:

P3 = ρMercury * g * h3 = 13,600 * 9.81 * 0.49 = 32,012.44 Pa

Next, let's calculate the pressure at point 2 (P2). Using the density of oil (ρoil = 850 kg/m^3) and the height h2 = 0.31 m, we have:

P2 = ρoil * g * h2 = 850 * 9.81 * 0.31 = 2,488.07 Pa

Finally, let's calculate the pressure at point 1 (P1). Using the density of water (ρwater = 1000 kg/m^3) and the height h1 = 0.16 m, we get:

P1 = ρwater * g * h1 = 1000 * 9.81 * 0.16 = 1,568.16 Pa

Now, we can calculate the gage pressure at point 1 by subtracting the atmospheric pressure. Since the question does not provide the value of atmospheric pressure, we cannot calculate the exact gage pressure. However, we can provide the equation to calculate it once the atmospheric pressure is known:

P1, gage = P1 - Patm

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