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MATH
DUNK
THE Supersoaker
Vocabulary - Supersoaker
Equilibrate: Equilibrate means to reach or maintain a state of balance or equilibrium.
Equilibrium: Equilibrium refers to a state of balance, where opposing forces or factors are equal and cancel each other out.
Flow rate: The measure of how quickly a fluid (such as water) moves through a particular area or opening.
Net worth: The value of a person's assets (such as money, property, investments) minus their liabilities (debts and obligations).
Nozzle: A narrow opening or spout through which a liquid or gas can flow.
Piston: A piston is a moving part in a cylinder that slides back and forth and is usually connected to a rod or crankshaft.
Prototype: A prototype is an early or preliminary version of something.
Reservoir: A place where something is collected and stored.
Volume: The amount of space occupied by an object or substance.
Volumetric: Volumetric refers to the measurement or calculation of volume.
The Science of Water Guns
by Drenchenator - Updated on (07/26/07)
edited & augmented by David Trotman (8/26/16)
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Background
Historically, water guns were made of metal and used rubber squeeze bulbs to load and propel water through a nozzle. Before the 1980s, water guns had fairly limited capabilities. Handheld pistols could only shoot water a short distance. They shot a weak, narrow stream and you had to refill them after every shoot-out.
The Classic Water Gun
Traditionally, water guns have worked on the same principle as a spray bottle. The body of the water gun is essentially a container for water and the trigger is attached to a pump which squirts water out of a tiny hole at the muzzle or nozzle.
In a classic squirt gun, there are just a few basic parts:
There is a trigger lever (A), which activates a small pump (C, D).
This pump is attached to a plastic tube that draws water from the bottom of the reservoir (E).
The pump pressures this water down a narrow barrel (F) and out a small hole at the gun's muzzle (G).
In order to equalize the pressure for the next shot, there is an air intake valve on the trigger (B).
In order to refill the gun, there is a hole (H) for replenishing the water supply.
Pressure
Pressure (P) is pressure per unit area. For our purposes, gases (in this case, the gas better known as air), apply pressure; liquids do not compress unless subjected to pressures unattainable by our means. By far, the most common unit for pressure is pounds per square inch (psi).
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Pressure is applied equally in all directions. Pressure is measured using two systems: absolute pressure and gauge pressure. Gauge pressure is the pressure displayed on a pressure gauge, the pressure difference between absolute pressure and atmospheric pressure. Absolute pressure adds atmospheric pressure (approximately 14.7 pounds per square inch) to gauge pressure.
Boyle's Law
At a constant temperature, Boyle's Law idealizes the relationship between a gas' pressure (P) and its volume (V). For a given amount of gas, if volume decreases, pressure increases. If volume increases, pressure decreases. This equation is useful because it models pressure as volume changes or volume as pressure changes. Again, note that Boyle's Law uses absolute pressure and applies only to gases.
Note: the subscript “0“indicates a time or status.
Utilizing the physics of Boyle’s Law, the traditional squirt gun sends out a stream of water when the trigger is depressed. The movement of the trigger apparatus back into the handle of the water gun, decreases the volume available for the water, the pressure increases, the water squirts out the nozzle, and then as the trigger is released, the stream of water stops, the pressure inside the gun decreases below atmospheric pressure and air rushes into to gun through a small hole in the barrel behind the trigger to restore a pressure equilibrium.
The Pump
The only complex element in this design is the water pump. The main moving element is a piston, housed inside a cylinder. Inside the cylinder is a small spring. To operate the pump:
You pull the trigger back, pushing the piston into the cylinder.
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This compresses the spring, causing it to push the piston back out of the cylinder when you release the trigger.
These two strokes of the piston, into the cylinder and out again, constitute the entire pump cycle.
The trigger pull, pushes the piston in, shrinking the volume of the cylinder, forcing water or air out of the pump. When the trigger is released, the spring pushing the piston back out, expands the cylinder volume, sucking water or air into the pump. In a water gun, it sucks water in from the reservoir below and pressures it out through the barrel above. In order to get all the water moving through the barrel, the pump must only pressure water up -- it cannot pressure water back into the reservoir. In other words, the water must move through the pump in only one direction.
The device that makes this possible is called a one-way valve. The one-way valve in a basic squirt pistol consists of a tiny rubber ball that rests neatly inside a small seal. There are two one-way valves: one between the reservoir and the pump, and another between the pump and the nozzle.
This pump design is has two big limitations;
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The amount of water in each blast is limited by the size of the pump cylinder. The size of the pump cylinder, in turn, is determined by the range of the trigger mechanism. To compress and expand more water, you have to push and pull the piston a greater distance, which means pulling the trigger farther back.
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The duration of the blast is also limited. Each pull on the trigger creates only a small burst. To squirt water continually, you have to keep squeezing and releasing the trigger.
The man who overcame these limitations is;
LONNIE JOHNSON
Nicknamed "The Professor" by his high school buddies, Johnson represented his high school at a 1968 science fair. The fair took place at the University of Alabama, where, just five years earlier, Governor George Wallace had tried to prevent two black students from enrolling at the school by standing in the doorway of the auditorium.
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The only black student in the competition, Johnson presented his compressed-air-powered robot, called "the Linex," built from junkyard scraps. Much to the chagrin of the university officials, Johnson won first prize. "The only thing anybody from the university said to us during the entire competition," Johnson later recalled, "was 'Goodbye' and 'Y'all drive safe, now.'
Johnson went on to join the U.S. Air Force, where he helped develop the stealth bomber program. Johnson moved on to NASA's Jet Propulsion Laboratory in 1979, working as a systems engineer for the Galileo mission to Jupiter and the Cassini mission to Saturn.
Johnson continued to pursue his own inventions in his spare time. One of his longtime pet projects was an environmentally friendly heat pump that used water instead of Freon (Freon is a gas coolant used to keep the food in your refrigerator from spoiling). Johnson finally completed a prototype one night in 1982 and decided to test it in his bathroom. He aimed the nozzle into his bathtub, pulled the lever and blasted a powerful stream of water straight into the tub.
Super Soaker Prototype
Johnson’s innovation was the first commercially successful water gun to use a pump to push air into a partially water-filled reservoir (in the picture of the prototype above, the reservoir is the clear plastic bottle). The reservoir is otherwise air-tight, but it has one valve to let the incoming air in from the pump (this is the lower of the two tubes), as well as a manually controlled valve operated by the user, commonly activated by pulling on a trigger. As more air is pumped in, the air in the reservoir is compressed, increasing in pressure; the water is also pressurized by the now compressed air. Upon opening the nozzle valve by pulling the trigger, the pressurized water is pushed out through the nozzle as the air attempts to re-equilibrate with atmospheric pressure. This system allows pumped in air pressure energy to be stored and used as needed. This system allows production of a solid, continuous stream of water.
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How much water do you need?
The volume of water pumped in the pressure chambers after a certain number of pumps is easy to calculate. As long as each stroke is full, the amount of water inputted into the any gun's chamber is the product of the number of pumps and the volume of water moved in each stroke.
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Vw =nVp
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Where V equals volume, w stands for water, n is the number of pumps, and p is the volume per pump.
In a standard air pressure water gun, such as the Super Soaker 50 pictured below.
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the pressure chamber has a set total volume. With both air and water occupying the chamber, the sum of the volume of air and water matches the entire chamber's volume. Pressure output relates to this equation, VC = VA+VW where V = volume, C = chamber, A = air, and W = water, and
Boyle's Law.
Total Chamber Volume
The chamber as pictured above, is a cylinder with rounded ends. You can determine the volume of such a shape by determining the volume of the cylinder. Its rounded ends when combined will be the shape of a sphere. The first equation determines the volume of a cylinder, the second the volume of a sphere.
Volume of a cylinder; V= πr2h – The volume of a cylinder equals π (pi) times the radius squared (the area of a circle) times the height of the cylinder.
Volume of sphere; V= 4/3πr3 – The volume of a sphere equals 4 divided by 3, times π (pi) times the radius of the sphere cubed.
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Design Improvements - A separate pressure / firing chamber
The air-based separate pressure chamber or firing chamber system works on the same physical principle as the pressurized reservoir system, but instead of pressurizing the reservoir, a separate, fixed volume chamber (see below, the rear yellow bulb) is included on the water gun into which water is pumped, compressing the air inside. This technology was first used on the Super Soaker SS 100.
This allows the reservoir to be removed/opened at any time for refilling since the reservoir is not pressurized. As well, the typically smaller size of the pressure chamber and the fact that water is typically pumped, as opposed to air, reduces the average number of pumps needed to achieve functional pressure.
Output
Output is the rate at which water shoots out of a water gun. In fluid mechanics, output is known as volume rate of flow. The units are in volume per unit of time. A common unit for rate of flow is gallons per minute (GPM).
Output is measured inconsistently in water gunning. Many describe output as the amount of water emitted during the first second of the shot. This method does not describe the shot as a whole because output is greatest at the beginning of a shot. For instance, air pressure guns have severe output drop-off.
Average output is the other common measure of output. The total water emitted is divided by the time taken. Many times, the shot does not last for an entire second or water shoots out at a significantly greater rate at the beginning of the shot. Average output depicts the shot as a whole.
By definition, output is the rate at which water leaves the soaker and pressure chamber as well. This point is often overlooked. Output is directly related to the amount of water in the gun.
Volume Flow Rate
Q=Av
This equation is known as the volumetric flow rate equation. In water gunning, it calculates stream velocity at the nozzle. Using the area of nozzle and the output rate, the stream exit velocity can be calculated.
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Average Output
As described earlier, average output is the volume of water shot out divided by the shot time.
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"Super Soaker", became a massively successful item. It topped $200 million in sales in 1991, and went on to annually rank among the world's best-selling toys. As of 2016, Lonnie Johnson net worth is estimated to be $360 million dollars.
STEM TOPIC 15: Problem Set - 1
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If a water pistol can hold 200 mL of water, and it takes 5 mL of water to fire one shot, how many shots can the water pistol fire before running out of water?
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If two people are having a water pistol fight, and each person has a water pistol that can shoot 3 shots per second, how many shots will be fired in 30 seconds?
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If a water pistol costs $10 and each refill costs $2, how many refills will you need to buy before the total cost of the water pistol and refills is $30?
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If a water pistol can fire 10 shots per second, how long will it take to empty a 2-liter water bottle if each shot uses 10 mL of water?
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If a water pistol can shoot water at a rate of 1 liter per minute, how long will it take to fill up a 10-liter bucket?
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If two people are having a water pistol fight and each person can fire 15 shots before needing to refill, how many total shots will be fired if they both keep shooting until they run out of water?
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If a water pistol has a diameter of 5 cm and a length of 20 cm, what is the volume of water it can hold?
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A water pistol shoots water in the form of a conical spray pattern. The diameter of the spray circle is 12 inches, and the height of the cone is 8 inches. What is the volume of space inside the spray pattern? volume of the cone = (1/3)πr2h
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A Super Soaker shoots water in a straight line. If the water jet forms an angle of 45 degrees with the ground, and it reaches a distance of 2 meters, how high was the muzzle at the start of the squirt?
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A water pistol has a cylindrical water tank with a height of 10 centimeters and a radius of 4 centimeters. What is the total surface area of the cylindrical tank?
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A Super Soaker has a water reservoir in the shape of a rectangular prism. The length is 20 centimeters, the width is 15 centimeters, and the height is 10 centimeters. What is the volume of the water reservoir?
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A water pistol sprays water in a circular pattern with a radius of 5 inches. What is the area of the circular water spray pattern?