Question regarding the differential height of mercury in a manometer

In summary, by converting the given values to their respective units, we can calculate the velocities at points 1 and 2 in a circular pipe. Using these velocities, we can then solve for the pressure difference between the two points, which is equal to the weight of the fluid column. By rearranging the equation, we can find the height difference between the two points, which in this case is 0.05m.
  • #1
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Homework Statement
Water flows upward through an inclined pipe with a 20-cm diameter at a rate of 1.5 m^3/min. The diameter of the pipe is then reduced to 10-cm. The pressure difference between the two pipe sections is measured using a mercury manometer. The elevation difference between the two points on the pipe where the two arms of the mercury between the two points on the pipe where the two arms of the manometer are attached is 0.2-m. Neglecting frictional effects, determine the differential height of mercury between the two pipe sections.
Relevant Equations
Bernoulli Eq:##p_{1} + \frac{1}{2}Pv_{1}^{2} + Pgy_{1}=p_{2} + \frac{1}{2}Pv_{2}^{2} + Pgy_{2}##
Where P= Density and p= pressure
Continuity: ##A_{1}v_{1}=A_{1}v_{2}= Q##
Given:
##y_{2} - y_{1}= 0.2m##
##Q= 1.5\frac{m^{3}}{min}##
##Q= 0.025\frac{m^{3}}{s}## After conversion
##D_{1}= 0.2m## After conversion
##D_{2}= 0.1m## After conversion
##r_{1}= 0.1m##
##r_{2}= 0.05m##
##p_{1} - p_{2} = \frac{1}{2}P(v_{2}^{2}-v_{1}^{2}) + Pg(y_{2}-y_{1})##

Calculating Velocity using circular Area of the pipe
##v_{1}= \frac{Q}{A_{1}}##
##v_{2}= \frac{Q}{A_{2}}##
##A_{1}=0.03142m^{2}##
##A_{2}=0.007854m^{2}##
##v_{1}= 0.7957\frac{m}{s}##
##v_{2}= 3.183 \frac{m}{s}##

Inputting

##p_{1} - p_{2} = \frac{1}{2}(1000\frac{kg}{m^{3}})((3.183\frac{m}{s})^{2}-(0.7957\frac{m}{s})^{2}) + (1000\frac{kg}{m^{3}})(9.81\frac{m}{s^{2}})(0.2m)##
##p_{1} - p_{2} =6710.9\frac{kg}{ms}##

My question is where do I go from here to find the height?
 
Last edited:
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  • #2
I found the height, and its 0.05m
 

Related to Question regarding the differential height of mercury in a manometer

1. What is a manometer?

A manometer is a scientific instrument used to measure pressure, typically in gases or liquids. It consists of a U-shaped tube filled with a liquid, such as mercury, and is used to compare the pressure of a gas or liquid to a reference pressure.

2. How does a manometer work?

A manometer works by balancing the pressure of a gas or liquid with the pressure of a reference column of liquid, typically mercury. The difference in height between the two columns of liquid is proportional to the pressure being measured.

3. What is the differential height of mercury in a manometer?

The differential height of mercury in a manometer refers to the difference in height between the two columns of mercury in the U-shaped tube. This difference in height is used to calculate the pressure of the gas or liquid being measured.

4. How is the differential height of mercury measured?

The differential height of mercury is measured by using a ruler or other measuring device to determine the difference in height between the two columns of mercury in the manometer. This measurement is then used in the equation to calculate the pressure.

5. What factors can affect the differential height of mercury in a manometer?

The differential height of mercury in a manometer can be affected by factors such as temperature, atmospheric pressure, and the density of the liquid being measured. It is important to control for these factors in order to get an accurate measurement.

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