Please help im stuck!!!! thank you!!! this is for computational methods mechanic

Question

Please help im stuck!!!! thank you!!! this is for computational methods mechanical engineering in the roots and open methods section

A water tower is connected to a pipe with a valve at its end as depicted in Fig. P6.39. Under a number of simplifying assumptions (e.g., minor friction losses neglected), the following energy balance can be written d d 2 where g = gravitational acceleration (= 9.81 m/s, h = tower height (m), u = mean water velocity in pipe (m/s), f= the pipe's friction factor, L = horizontal pipe length (m), d: pipe diameter (m), Le,e equivalent length for the elbow (m), Lev equivalent length for the valve (m), and K loss coefficient for the contraction at the bottom of the tank. Write a MATLAB script to determine the flow exiting the valve, Q (m3/s), using the following parameter values: h 24 m, L 65 m, d- 100 mm, Le, eld = 30, Ledd-8, and K = 0.5. In addition, the kinem aticiscosity of water is = 1.2 x 10-6 m2/s. FIGURE P6.39: A water tower connected to a pipe with a valve at its end. 0

Explanation / Answer

Below is the matalb code, for calculating the pressure difference from height 'h' to ground level I have used Bernoulli's theorem (Dp=rho*g*h) and then I have used Darcy's equation (for calculating the frictional losses in pipe 'f' can be calulated from the formula provided in the question itself) for calculating the mean velocity of the flow and then multiply that velocity with the area od pipe we get the flow rate.

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clear all;clc;

% you can calculate the 'f' from the formula provided in question
g=9.81;
h=24;
L=65;
d=.1;
L_eed=30;
L_evd=8;
K=0.5;
v=1.2*10^-6; % kinematic viscosily
rho=1000;
mu=1.2*10^-6*rho; % dynamic viscosity
f=(g*h-(v^2/2))/((((L+h)/d)+L_eed+L_evd)*v^2/2+K*v^2/2);

% pressure drop
Dp=rho*g*h

% from darcy formlula for laminar flow, we get the mean velocity
v=Dp*2*d/(L*rho*f);

% flow rate
A=(pi*d^2)/4;
Q=v*A;

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