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Problem 3.29 PDF

The document provides a problem involving calculating the deflection, l, of a U-tube manometer connected to an open tank filled with water. It states the given values of the dimensions and specific gravities. It then outlines the relevant hydrostatic pressure equations and assumptions. The solution sets up and simplifies the hydrostatic balance equation relating the pressure changes across the manometer legs. This allows isolating l and solving for the manometer deflection of 1.600 m.

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Kauê Britto
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200 views1 page

Problem 3.29 PDF

The document provides a problem involving calculating the deflection, l, of a U-tube manometer connected to an open tank filled with water. It states the given values of the dimensions and specific gravities. It then outlines the relevant hydrostatic pressure equations and assumptions. The solution sets up and simplifies the hydrostatic balance equation relating the pressure changes across the manometer legs. This allows isolating l and solving for the manometer deflection of 1.600 m.

Uploaded by

Kauê Britto
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Problem 3.

29 [Difficulty: 2]

Given: A U-tube manometer is connected to the open tank filled with water as
shown (manometer fluid is Meriam blue)
D1 = 2.5⋅ m D2 = 0.7⋅ m d = 0.2⋅ m SGoil = 1.75 (From Table A.1, App. A)

Find: The manometer deflection, l

Solution: We will apply the hydrostatics equations to this system.

Governing Equations: dp
= ρ⋅ g (Hydrostatic Pressure - h is positive downwards)
dh
ρ = SG⋅ ρwater (Definition of Specific Gravity)

Assumptions: (1) Static liquid


(2) Incompressible liquid

Integrating the hydrostatic pressure equation we get:

Δp = ρ⋅ g⋅ Δh

When the tank is filled with water, the oil in the left leg of the manometer is displaced
downward by l/2. The oil in the right leg is displaced upward by the same distance, l/2. D1 d d
Beginning at the free surface of the tank, and accounting for the changes in pressure with
elevation:
D2 c
patm + ρwater⋅ g⋅ ⎛⎜ D1 − D2 + d + ⎟ − ρoil⋅ g⋅ l = patm
l⎞
⎝ 2⎠
Upon simplification:
D1 − D2 + d
ρwater⋅ g⋅ ⎛⎜ D1 − D2 + d +
l⎞ l
⎟ = ρoil⋅ g⋅ l D1 − D2 + d + = SGoil⋅ l l =
⎝ 2⎠ 2
SGoil −
1
2

2.5⋅ m − 0.7⋅ m + 0.2⋅ m


l = l = 1.600 m
1
1.75 −
2

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