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Math Help - Fire Hose (Linear... Wrong Answers)

  1. #1
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    Fire Hose (Linear... Wrong Answers)

    If a fire hose is held horizontally, then the distance the stream will travel depends on the water pressure and on the horizontal factor for the nozzle. The horizontal factor H depends on the diameter of the nozzle. For a 0.5-inch nozzle, the horizontal factor is 56. For each 1/8-inch increase in nozzle diameter, the horizontal factor increases by 6.

    (a) Explain why the function giving the horizontal factor H in terms of the nozzle diameter d (measured in inches) is linear.

    (Because the horizontal factor H always increases by 6, when d increases by 1/8, the horizontal factor has a constant rate of change.)

    (b) Use a formula to express H as a linear function of d.

    H= \frac{1}{8}d+6

    (c) Once the horizontal factor H is known, we can calculate the distance S in feet that a horizontal stream of water can travel by using the following formula where p is pressure in pounds per square inch.

    S=\sqrt{Hp}

    How far will a horizontal stream travel if pressure is 45 pounds per square inch and the nozzle diameter is 1.75 inches? (Round your answer to one decimal place.)

    8.9

    (Of course... all of these answers are wrong... what am I doing?)
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  2. #2
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    Hint for (b): if H increases by 6 when d increases by 1/8, what does H increase by when d increases by 1? Also, use the fact that H(1/2) = 56.
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  3. #3
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    fire hose

    Quote Originally Posted by icemanfan View Post
    Hint for (b): if H increases by 6 when d increases by 1/8, what does H increase by when d increases by 1? Also, use the fact that H(1/2) = 56.

    Ahead of water @45psi (103.9 ft) has a potential energy of 103.9 ft equivalent to a velocity head of 81.8 fps. A well rounded nozzle will produce about 98% of that. Since water leaving. the nozzle falls @32.2fps/s you can calculate the time it will hit the ground knowing the nozzle elevation.Then this time xapprox 80 equals the horizontal distance.Nozzle size is not a factor.



    bjh
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