Measuring Atmospheric Pressure and Altitude with Water Hose Barometer

The higher a place the lower it’s atmospheric pressure. If air pressure is known then the height can be calculated, and vice versa if the altitude is known then the air pressure can be calculated.

The following formula shows the relationship between pressure and altitude:

where h is altitude height in meter, and the constant parameters are as described below:

Parameter	Description	Value
p0	sea level standard atmospheric pressure	101325 Pa
L	temperature lapse rate	0.0065 K/m
T0	sea level standard temperature	288.15 K
g	Earth-surface gravitational acceleration	9.80665 m/s2
M	molar mass of dry air	0.0289644 kg/mol
R	universal gas constant	8.31447 J/(mol•K)

If no barometer is available then we can use a water hose and a bucket of water to measure air pressure. Prepare a transparent water hose with about 12 meters length, with diameter 3/8 inches, greater diameter will be expensive. Prepare a bucket, 10 liter bucket can do, fill the bucket with water up until full. Put that bucket of water at high position, eg on a table. Dip one end of the hose into the bucket, put a weight at this end of hose to make it keep submerged in water, make sure this submerged hose end always open. Position the other end of the hose slightly lower than the bucket, then suck this hose end to pump water out of the hose or become a siphon. Make sure the water out smoothly, ensure there is no air bubble inside the hose.
 

Close the end of the hose where the water came out, can use plastic sheet and rubber bands. Lift this sealed hose end until it reaches 10 meters height. Make sure the other end of the hose remains submerged in the bucket and keep it open. Water inside the hose will go down as water is being attracted by the gravity force. But the water is also pushed up  air pressure on the surface of water in the bucket, the air pressure to push water up the hose to fill the empty space on the upper end of the hose. Gravity force versus air pressure on the water will form a column of water in the hose.
 

Measure the height of water column of water formed in the hose that stands upright, C on the above picture. Water column height represents the air pressure at the surface of the water on the bucket, the bucket position altitude from sea level can be calculated by the formula above.

This Barometer is quite accurate as it has a very lenght scale, reaching 10 meters or 10,000 mm. For every 1 meter increase of water bucket altitude, water column will drop about 1 mm. But because of its large size it is not practical to carry around.

The following table shows the relation between altitude and atmospheric pressure (water column), eg. if the water column height is 9 meters H₂O in the hose, then the height (altitude) is about 1,150 meters from sea level. The above formula produces pressure in Pascal units, conversion of 1 Pascal = 0.000102 meters H₂O. Please note that the Altitude in meters, whereas C in meters with 3 digits after the decimal point.

Altitude meter	Pascal	C meter H2O
0	101,325	10.335
300	97,773	9.973
600	94,322	9.621
900	90,970	9.279
1,150	88,252	9.002
1,500	84,556	8.625
1,800	81,490	8.312
2,100	78,513	8.008
2,400	75,626	7.714
2,700	72,825	7.428
3,000	70,109	7.151
3,300	67,475	6.882
3,600	64,922	6.622
3,900	62,448	6.370
4,200	60,051	6.125
4,500	57,729	5.888
4,800	55,480	5.659
5,100	53,303	5.437
5,400	51,195	5.222