Build Your Own Manometer

An activity from the Burroughs Wellcome Student Research Program
Flight: From Butterflies to Boeing

How it Works
A manometer measures the speed of air based on Bernoulli's Principle.As the fast moving air moves over the tube opening at C, low pressure is created. The higher pressure at A, where the air is still, pushes the water up the tube. As the speed of the air at C increases, the difference in pressure between A and C also increases and work is done on the water to push it up the tube (B).

Making a Manometer:
You will need at least15 inches of clear flexible rubber tubing Scotch tape 6" by 12" (or longer) piece of cardboard ruler colored water pipette scissors stiff paper such as card stock or construction paper

Assemly Instructions

1. Attach the tubing to your cardboard using Scotch tape. Use the entire length of your cardboard. Make sure the tubing reaches from the bottom to the top and makes a J shape. To make you life easier later, make the curve at the bottom as tight as possible.
   
2. Use a scrap piece of cardboard to make and attach a support for the manometer. All of the speed values have been calculated for a 30 degree incline from the horizontal. (This basically cuts the effect of gravity in half so that the distance the water rises is double for a given speed then if the manometer were held vertically.) Your manometer is at a 30 degree angle when the height is half the length.
   
   
3. Use a dropper to pour colored water into the rubber tubing. Be VERY careful not to let any bubbles in the tube. If this happens, pour or blow the water out and try again. Dropping the water in a quick continuous stream works best. You want enough water to fill the curved part of the J.
   
   
4. Make a guard to protect the lower part (A) of the tube from the moving air. Fold a piece of stiff paper in half (1). Then fold the outside edges in the opposite direction (2) to form a base.
   
   Fold the rest of the guard in half again to make it sturdier. Cut a small hole for the long end of the tube to pass through. Attach the guard to your cardboard so that is protects the lower part of the tube from the fast moving air and keeps it at atmospheric pressure.
   
   
5. On the long end of the tube, mark the water level. Label this as 0 miles/hour. Use your ruler and the table below to make a scale for your manometer.
   
   
6. Try it out! Blow across the top of the tube at C. How high can you make the water rise? Try using a hair dryer or leaf blower with multiple settings as well.

DO NOT BLOW INTO THE TUBE!!!
All of the water will come out the other side!
Calibration Table

Change in Height (inches)	Air Speed (feet/sec)	Air Speed (mph)
0.5	47	32
1	66	45
1.5	81	55
2	94	64
2.5	105	71
3	115	78
3.5	124	84
4	132	90
4.5	140	96
5	148	101
5.5	155	106
6	162	110
6.5	169	115
7	175	119
7.5	181	124
8	187	128
8.5	193	132
9	198	135
9.5	204	139
10	209	143
10.5	214	146
11	219	150
11.5	224	153
12	229	156
12.5	234	159
13	239	163

This table was formed using Bernoulli's Equation:

(¹/₂ d_Av_A²) + (g h_Ad_A) + P_A = (¹/₂ d_Bv_B²) + (g h_Bd_B) + P_B

Here the subscript A refers to the fluids (fast moving air) outside the tube and subscript B refers to the fluid inside the tube. P refers to the pressure of the fluid, v is the velocity, d is the density, g is the acceleration due to gravity and h is the height of the fluid.

Since the air outside the tube and inside the tube both reach the same height (the top of the tube) and have the same density, the second terms on both sides cancel out leaving:

(¹/₂ d_Av_A²) + P_A = (¹/₂ d_Bv_B²) + P_B

Also, the air inside the tube is not moving so its velocity is zero and we can drop that term also:

(¹/₂ d_Av_A²) + P_A = P_B

The pressure on the air inside the tube is equal to the pressure of the air outside the tube added to the pressure of the water:

P_B = P_A + (g h_waterd_water)

By combining the last two equations we get:

(g hd_water) = (¹/₂ d_airv_air²)

where the subscript water refers to the water in the tube, the subscript air refers to the fast moving air outside the tube and the h is the change in height.

NOTE: To account for the fact that the water on the right hand side moves down just as much as the water on the other side moves up you should multiply the height by 2. However, to account for mounting the manometer at a 30 degree angle you should divide the height by 2. These two processes cancel each other out so we can leave the equation as is.

The calibration table was formed using the last equation and the following values:

gravitational acceleration (g) = 32.2 ft/s²
density of air (d_air) = .0755 lb/ft³
density of water (d_water) = 62.4 lb/ft³
and the change in height is measured off the manometer.

 

Reference: University Physics: Models and Applications, William P. Crummett & Arthur B. Western, Wm C. Brown Publishers, 1994, page 430.