Bernoulli Equation States that for an Incompressible Fluid - Mathematics Assignment Help

Assignment Task:

Task:

PROBLEM:
Bernoullis equation states that for an incompressible fluid the following summation is constant across the flow: v^2/2 + g*z + P/rho, where v = fluid velocity, g = gravitational constant, z = elevation, P = pressure, and rho = density (constant throughout the fluid due to incompressible nature). The values of v, z, and P change at points along the flow whereas values for g and rho are assumed constant.

Assuming all units are congruent, fill in the holes (zero values) in the given matrix of v, z, and P values, in three respective rows for n measured points (3 x n matrix). Use g = 9.81. Rho will be given for each test case. The input matrix will contain one complete set of values to calculate the constant. The completed matrix will not contain any zeros (or very small numbers).

Test 1
Code Input
%%
in = [1 0.6 0.8 1 1; 1 1.1 1.2 1.3 1.4; 10 0 0 0 0];
rho = 1.0;
out = [1 0.6 0.8 1 1; 1 1.1 1.2 1.3 1.4; 10 9.339 8.218 7.057 6.0760];
eps = 1e-3;
assert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) < eps)
TEST 2
Code Input
%%
in = [1 0.6 0.8 1 1; 0 0 1 0 0; 10 12 10 14 8];
rho = 1.5;
out = [1 0.6 0.8 1 1; 0.9817 0.8784 1 0.7098 1.1176; 10 12 10 14 8];
eps = 1e-3;
assert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) < eps)
TEST 3
CODE INPUT
%%
in = [0 0 0 1 0; 1 1.1 1.2 1.3 1.4; 10 12 10 14 8];
rho = 0.75;
out = [4.1896 3.2027 3.6917 1 3.8779; 1 1.1 1.2 1.3 1.4; 10 12 10 14 8];
eps = 1e-3;
assert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) < eps)
TEST 4
CODE INPUT
%%
in = [1 1.6 0.8 1 1 0 0 1 1 1.2; 1 1.6 0 1.3 0 1.9 1.8 1.7 0 1.8; 0 12 5 0 8
7.5 7.7 0 11.1 0];
rho = 0.97;
out = [1 1.6 0.8 1 1 2.4397 2.7390 1 1 1.2; 1 1.6 2.4335 1.3 2.0999 1.9 1.8
1.7 1.7741 1.8; 18.466 12 5 15.6113 8 7.5 7.7 11.805 11.1 10.6401];
eps = 1e-3;
assert(sum(sum(abs(Bernoulli_eq(in,rho)-out))) < eps)

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