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MATLAB Water Delivery System with Newtons Method

  1. Feb 13, 2012 #1
    1.We are asked to:
    i - Plot Wdot(pump) vs Q where v varies from 1 m/s to 50 m/s in increments of 1 m/s
    ii - plot P vs Q
    iii - write a function that uses newtons method with a numerical derivative to calculate the friction factor -- function f = frict (e_over_d,Re)

    equations are below



    In this program you will write a program that determines the pressure a pump must provide and the horsepower required to run an ideal pump for a system that removes water from a reservoir and discharges the water to a second water reservoir at a higher elevation.
    water density ρ = 998 kg/m^3
    water viscosity μ = 1.003E-3
    roughness ratio e/D= 2E-4
    g = 9.81 m/s^2




    2. pump exit pressure, P
    P = ρ[f*(L/D)*(v^2/2) + g*h]/b]

    Colebrook equation for the friction factor f (based on Re=*v*D/μ)

    1/√f = -2log(base10)[(ε/D*3.7)+(2.51/Re*√f)] which when solved for f (neglecting the f term on the right side of the equation) => f = 1.325/[ln(ε/3.7D + 5.74/Re^.9)]^2

    horsepower for the pump

    Wdot(pump) = mdot [P/ρ + v^2/2]



    3. I created a for loop for the Reynolds number:
    clc
    clear all

    rho=998;
    mu=1.003e-3;
    D=.5;
    v=1:1:49;
    Re=rho*v*D/mu;
    i=0;
    for i=1:length(v)
    i=i+1
    v=i;
    Re=rho*v*D/mu
    root(i)=funct(v(i))
    end

    Now i need to figure out how to call this loop into another loop using the friction factor equation f..

    Once i get that i need to plug that f value "loop"(from 1 to 50 m/s for velocity of course) into the Pressure function and then that P loop into the Wdot(pump) equation so I can plot it..

    newtons method is applied here but I dont understand why because I am not taking derivative. The only thing i can think of is that since v changes by 1 m/s up to 50 m/s so its a rate of change. It will keep going up by adding small parts together with newtons method which is this code:
    function [ f ] = frict( e_over_d,Re )
    %use secant method to calculate the friction factor
    % Detailed explanation goes here
    e_over_d=2e-4;
    rho=998;
    mu=1.003e-3;
    vo=1;
    D=.5
    Re=rho*vo*D/mu;
    f =1.325/(ln((e_over_d/3.7)+(5.74/Re^.9))^2);
    eps=abs(f);
    iter=0;
    while eps>1.0e-12 && iter < 100

    fprime=1.325/(ln((e_over_d/3.7)+(5.74/Re(vo)^.9))^2);
    iter=iter+1
    delx=1.0e-4*vo
    vright=vo+delx
    fright=1.325/(ln((e_over_d/3.7)+(5.74/Re(vright)^.9))^2)
    fprime=(fright - f)/delx
    v = vo-f/fprime
    f= 1.325/(ln((e_over_d/3.7)+(5.74/Re^.9))^2);
    eps=abs(f)
    v=vo



    end

    this code is all messed up but the format is newtons method.. I just cannot figure out how to use that Re loop i made with that function!!

    help!



    3. The attempt at a solution

    -Ethan G
     
  2. jcsd
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