[Basic Hydraulics] The Pitot Tube/Manometers

In summary, the problem is to determine the flow rate, Q, for a system with a 100 mm pipe and a 75 mm pipe, where the fluid in the pipe is water and the fluid in the metre is mercury. The S.G. of mercury is approximately 13.6 and the height difference of the mercury columns is 80mm. The equations used are Bernoulli's Equation and the Equation of Continuity, and the unknown height is canceled out when the left and right sides are equated. The right hand side also includes an additional term caused by the opening in the flow, which is the V^2/(2*g) term.
  • #1
MarleyDH
26
0

Homework Statement



Determine the flow rate, Q.

Ignore energy losses.

Given:

D1 = 100 mm
D2 = 75 mm
Fluid in the pipe is water.
Fluid in the metre is mercury.
S.G. of Mercury is ~13.6.
The difference in height of the mecury columns is 80mm.

Diagram is below.

t8mfz4.jpg


Homework Equations



Bernoulli's Equation.

Equation of Continuity. (Q1 = Q2)

The Attempt at a Solution



I approached this as a manometer question, but with that orifice in the flow I was unsure on how to proceed. I chose a datum as the lower of the two levels of mercury. The expressions I got were:

Px-x = Pressure due to the flow + Pressure due to the height of the water above the mercury + the pressure due to the mercury above the datum. This was for the left hand side.
Px-x = P1 + ρwgh + ρmgh', where h' = 80 mm and h is an unknown height which cancels out when the left side and right side are equated.

For the right hand side I said

Px-x = Pressure due to the flow + Pressure due to the height of the water.
Px-x = P2 + ρwg(h+h')

For this second equation I feel there is something missing, surely that opening in the flow causes an additional term to be added?
 
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  • #2
The tube on the right is facing the flow so it is measuring total pressure. You should include the V^2/(2*g) term. The water must come to a stop at the mouth of the tube. Pressure generated is V^2/2g.
 

FAQ: [Basic Hydraulics] The Pitot Tube/Manometers

What is a Pitot Tube and how does it work?

A Pitot Tube is a device used to measure the velocity of a fluid, typically air or water. It works by using the principle of Bernoulli's equation, which states that as the velocity of a fluid increases, its pressure decreases. The Pitot Tube has a small opening facing the fluid flow, and a larger opening perpendicular to the flow. By measuring the difference in pressure between the two openings, the velocity of the fluid can be calculated.

What is the purpose of a Manometer in a hydraulic system?

A manometer is used to measure the pressure of a fluid in a hydraulic system. It works by using a U-shaped tube filled with a liquid, typically water or mercury. The pressure of the fluid in the system causes the liquid in the tube to rise on one side, and by measuring the difference in height, the pressure can be determined. Manometers are commonly used in hydraulic systems to monitor and adjust pressure levels.

What are the different types of Manometers?

There are several types of manometers, including U-tube manometers, well manometers, and inclined manometers. U-tube manometers are the most common and consist of a U-shaped tube partially filled with a liquid. Well manometers have a larger reservoir of liquid and are used for measuring very low pressures. Inclined manometers use a tube that is not vertical, which allows for more precise measurements of small pressure differences.

What are some common applications for Pitot Tubes?

Pitot Tubes are commonly used in aerodynamics and fluid dynamics research, as well as in aircraft and spacecraft to measure airspeed. They are also used in weather instruments, such as anemometers, to measure wind speed. In industrial settings, Pitot Tubes are used to measure the flow rate of liquids and gases in pipelines.

Are there any limitations or potential sources of error when using Pitot Tubes and Manometers?

Yes, there are a few limitations and potential sources of error when using Pitot Tubes and Manometers. For Pitot Tubes, the location and orientation of the tube can affect the accuracy of the measurements. Contamination of the tube opening can also lead to inaccurate readings. For Manometers, changes in temperature and atmospheric pressure can affect the readings. Additionally, the type of liquid used in the manometer can also impact accuracy. Regular calibration and proper use can help minimize these sources of error.

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