That's not a typo in the title. The TV today holds such little entertainment for me that I find watching episodes of cartoons like "Spongebob" relaxing {the title comes from such an episode}.
That's me in the above photo, circa 1943, playing with a water wheel model my grandfather built. He was a self educated engineer. My dad was a professional engineer, and I was expected to follow suit. Well, I graduated with an MS in engineering but ended up for a large part of my adult life teaching high school physics instead. This was much to the chagrin of my dad who held to that old adage: "Those who can't do, teach".
Ok, so what this blog is about is based on my background as a physics teacher/engineer. Today I find interesting measurement applications around the home that some, especially those teaching science and/or physics, may be interested in.
The first of these pertains to that springy garden hose they're selling these days. It is a very lightweight hose that expands in length under pressure. I call this one: "Hooke's Hose". Treating the hose like a extension spring, its spring constant, k, can be measured. This is the first objective.
Unfortunately, I understand that theses hoses don't last very long when used as expected. Therefore, if you don't have one already, purchase the least expensive available. It's only necessary to measure one section of a multi-section hose, so the shortest length hose will work fine.
The other equipment needed for this hose test, will be: 1) tape measure and 2) a hose cap.
The pressure gage in photo below is not necessary. Some (myself included) may want to 'jury rig' a gauge like that shown for demonstration purposes.
How to Measure Hose (house) Pressure:
If the home where this test will be carried out has a city/town water supply. Then there is a water pressure gauge indicating house pressure usually found where the water line enters the house. Here hose pressure can be directly read from this in-house gauge. Just be sure that no other device that uses water is operating at the time of the test.
If the home has a well water pump system then there will be a pressure gauge on the water reservoir tank. This tank gauge should be read after the springy hose has been completely pressurized, and is at its fully expanded length. Measuring the water pressure at the proper time is more critical when a well pump is involved. This because the water pressure of such a system routinely varies, So, in this case, it is especially important that no other devices in the house that use water operate during the time when the hose expanded length and the reservoir tank pressure are measured.
For class demos, having a pressure gauge actually installed at one end of the hose is more convenient. I had one and simply "press fit" it onto a short piece of washing machine connecting hose (female end). The hose clamp shown in the photo wasn't large enough to go over the end of the gauge and hose so was effectively useless. However, the hose was a very tight fit over the gauge's outlet which didn't leak, even without the clamp, and a under hose pressure of 42 psi.
Hose Measurement Process
First lay out the hose or one section of a multi-section hose on a flat surface like a driveway in such a way that it is fully spread out lengthwise. Don't pull or otherwise put any tension on it when measuring its unexpanded length.
The measurement of unexpanded length should not include any unexpanding parts of the hose such as the end fittings. For reference, the unexpanded length of the hose I measured was 18 ft 7 in as seen in the photo below.
Next the hose is either blocked at the far end with a hose cap or a pressure gauge arrangement like the one I built. The other end of the hose is then connected by means of a second hose to a water spigot. The second hose is needed so that the entire length of the expanded hose can remain flat for ease of length measurement.
In my case, the fully expanded hose measured: 44 ft 3 in as seen below in this photo.
The Pressure (P) read by the gauge was 42 psi, and that has to be converted to a Force (F) acting to stretch the spring-like hose. I estimated the Diameter (D) of the hose to be 1/2 inch. That is the inside diameter of the end cap that can be used to seal the end of the hose. From this measurement, the cross-sectional Area (A) of the expanded hose is calculated. A = πD²/4 = π(0.5)²/4 = 0.196 in²
The Math:
The amount my hose was stretched (x): 44 ft 3 in - 18 ft 7 in = 25 ft 8 in = 25.7 ft
This cross-sectional area of hose = A = 0.196 in²
The force of the water that stretches the hose: F = P•A = (42)(0.196) ≈ 8.25 lbs
Hooke's Law: F = kx
{where x = expanded length of hose = 25.7 ft}
k = F/x = 8.25/25.7 ≈ 0.32 lb/ft
Going a Bit Further:
Normally for solid objects, like springs, a graph of force (F) versus extension (x) is drawn. The F is directly proportional to x, so that graph is a straight line with its slope = k. In the case of the springy hose, it is more useful to draw a graph of water pressure (P) versus extension (x). This graph too, can be a straight line, if we make an assumption.
The assumption that must be made is that the springy hose's radial expansion is small enough to ignore. In other words, the cross-sectional area (A) of the hose remains fairly constant regardless of the pressure. This seems like an acceptable assumption because the hose's diameter doesn't increase by an amount that the eye can detect.
Since F = kx and F = P•A then P•A = kx and P = (k/A)x {where k/A is constant = c}
Using my measurements as example: c = (0.32/0.196) ≈ 1.6 psi/ft
This means for every 1.6 psi increase in hose pressure, the hose will increase its length by 1 ft.
A graph can then be created of water pressure (P) vs overall hose length.
(I did this for my hose below):
Some Possible Graph Answered Questions:
1) Suppose this hose was sold as a 30 ft hose, what minimum pressure must exist in it to be that long?
2) If this hose is closed at one end (nozzle shut off) but it's connected to a well water pump system whose pressure varies between 40 psi and 60 psi, what is the length change created?
3) A gardner is trying to water the garden that is 40 ft from the hose spigot. The spray nozzle being used reduces the pressure in the hose by 20 psi. What must the spigot pressure be in order for the hose to reach the garden.
4) If a hose is made up of two of these same length hose segments (ignore length of non-expanding connectors) and water flowing through hose reduces the pressure by 30 psi, how far can the hose reach when connected to a water source at 55 psi?
5) If a hose of two of these same length hose segments is sold as a 100 ft hose, and the average water flow through the hose reduces hose pressure by one half that of the water supply pressure. What minimum supply pressure will guarantee the hose length to be as advertised?
