We have done an experiment and measured different pressures in a system, and are required to calculate the minor head loss coefficient K for our working sections.

The experiment layout can be seen here:

For the gradual working section at the entrance (LHS, where the pipe is beginning to expand), I have ended up with a negative K value.

This indicates a head gain, and I am wondering how is this possible? Have I done my calculations incorrectly?

Rearranging the energy equation I have the following:

K = (P1 - P2)/(500 * V^2) + (V1^2 - V2^2)/V^2, where rho was 1000 and hence divided by 2 to get 500

The values I got were:

P1 = 6534.631Pa

P2 = 7346.655Pa

V = 1.65075m/s (calculated from the pitot tube)

V1 = 1.170615m/s (calculated from the flowrate, thus V1 = Q/A1)

V2 = 0.169037m/s

Using the formula above and these values, you get:

K = -0.10359

The diameters are:

Pitot: 16mm

D1 = 19mm

D2 = 50mm

I am wondering if I am not understanding something for a practical model? Is the V value I am using correct? I understand there should be some more loss due to major head loss as well as minor loss from the elbow joint, thus lowering this V velocity value, but all that does is decrease my K value further.

My calculations for the sudden working section appear to have worked out.

tl;dr - Is this negative K simply something I can chalk up to measurement/experimental error, or is there something I'm missing?

Thanks in advance!