# Calculate Minor Losses due to Flow Geometry Alone

• I
• Timtam
In summary, the conversation discusses the calculation of minor losses related to flow geometry and the possibility of obtaining a formula that only takes into account area and velocity change. It also addresses the role of viscosity in these calculations and whether using a lower viscosity fluid could reduce minor head losses. The speakers also touch on the concept of inviscid flow and its implications on head loss calculations. Ultimately, there is no first principles formula for these calculations and they are primarily based on empirical data.
Timtam
Hi does anyone know a way to calculate the Minor losses related just to flow Geometry isolated from Major frictional losses, all the k tables I can find combine the frictional losses with the geometry losses eg see below blurb from

but I was hoping to obtain a first principles formula that could equate these losses solely to area and velocity change

The reason being is I am assuming that major losses component of the K values must be based on particular viscosity fluid but I would like to calculate this for different viscosity fluids ?

Also for the Darcy Weisbach if I want to calculate just the frictional losses would I use the average diameter of a convergent or divergent section of pipe ?

If such a formula exists it ok to just plain add these two effects ?

Am I making life to difficult for myself is there an easier way ?

There's really nothing about these sorts of head loss calculations that comes from first principles. It is basically all empirical.

But here is a more fundamental issue: if there was no viscosity at all, what do you think would cause such losses to occur in these sorts of situations?

This is what confuses me. I always thought that minor losses are (like major head loss ) also proportional to the viscosity of the fluid but I am seeing statements like the below that suggest that it isn't.

where KL means (local) loss coefﬁcient. Although KL is dimensionless, it is not correlated in the literature with the Reynolds number and roughness ratio but rather simply with the raw size of the pipe.

In an inviscid flow I was assuming that these Minor head losses come from the force required to change the Momentum of the flow or the orthogonal area the obstruction presents to the flow.

That said it makes sense to me that a lower viscosity fluid would find it easier to change direction and thus would incur smaller later flow separation

Is this correct ? could I also reduce my Minor head loss ( as well as my Major head loss) by using a lower viscosity fluid ?

The broader point I was trying to make is that an inviscid flow would incur no losses. Separation doesn't really make sense as a concept without viscosity. So, there is no source of dissipation to cause losses in an inviscid flow. Sure a force is required to accelerate the flow through a contraction, but that comes from a pressure gradient, and that pressure gradient is completely reversible in an inviscid flow. It's basically Bernoulli's equation.

## 1. What are minor losses due to flow geometry?

Minor losses refer to the pressure drop that occurs in a fluid flow due to changes in the shape or size of the flow path. These losses are caused by factors such as bends, valves, fittings, and contractions/expansions in the flow path.

## 2. How do I calculate minor losses due to flow geometry?

To calculate minor losses, you can use the Darcy-Weisbach equation, which takes into account the factors mentioned above. This equation is: hL = K*(V^2/2g), where hL is the head loss, K is the minor loss coefficient, V is the fluid velocity, and g is the gravitational constant.

## 3. What is the minor loss coefficient?

The minor loss coefficient, also known as the K factor, is a dimensionless value that represents the amount of pressure drop caused by a particular flow geometry. It takes into account the shape, size, and roughness of the flow path and is typically determined experimentally.

## 4. How does the flow rate affect minor losses due to flow geometry?

The flow rate has a direct impact on the minor losses due to flow geometry. As the flow rate increases, the velocity of the fluid also increases, resulting in higher pressures and consequently, higher minor losses. This is why it is important to consider the flow rate when calculating minor losses.

## 5. What are some common examples of minor losses in fluid flow?

Common examples of minor losses include sudden contractions or expansions, elbows, valves, and other fittings in a pipe system. These changes in the flow path can cause significant pressure drops and affect the overall efficiency of the system.

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