How to calculate total dynamic head (TDH) pressure difference

Bernoulli’s equation and Moody chart

TDH = ∆P_{p}+∆P_{s}+∆P_{v}+∆P_{fr}

Step 1

Calculate the pressure difference (∆P_{p}) by subtracting the target tank pressure in pascal from the source pressure.

Step 2

Calculate pressure loss due to static height differences (∆P_{s}).

Choose where is your zero height level where you like. It is advised to place it at the lowest point to avoid a negative height values. Any point under the zero height point will have a negative height value in meters (e.g. -7m).

Convert the density if necessary to kilogram divided by meter cube

(how to convert unites – click here).

Place the values into the equation (don’t forget to enter the g value).

Step 3

Calculate pressure loss due to velocity (∆P_{v}).

If the flow rate is give in cubic meters per hour or any other time unit you need to the convert volumetric flow rate to linear (m/s).

Calculate the vessel area via A = r^{2 }* π (A – area – m^{2} ) ( r – radius – m)

Enter the values to the equation below.

Remember to convert hours to seconds (how to convert unites – click here).

Now all you need is to plug the linear velocity value (v) into the (∆P_{v}) section of the equation above with the liquid density (e.g. water ~1000 kilograms per meter cube). If you are not asked to take into account the friction loss you are done.

Step 4

In order to calculate the pressure loss due to friction differences (∆P_{fr}) you need to calculate Reynolds number and relation (ratio) between the diameter of the pipe (d) to the roughness of the pipe commonly noted as k, use the Moody diagram to find the friction factor λ, sum the resistivity number ζ and plug the other values into the ∆P_{fr} section of the equation above.

To calculate Reynold number you will need to identify the kinematic viscosity. What is Kinematic viscosity? Kinematic viscosity is the bullied in so to say resistance of a fluid. Kinematic viscosity units are **m ^{2}/s** which can be very censusing with the linear flow rate because of their similar sign and units. Linear flow rate units are

**m/s**.

figure from the blog “ALL ABOUT MECHANICAL ENGINEERING” thermix.net

Insert the linear flow rate, the diameter (in meters) and the kinematic viscosity to this equation to calculate Reynolds number.

Calculate the ratio (unitless) between the diameter (d) to the roughness constant (k). Make sure that the units match. k is usually given in mm (milometers). The bigger the ratio the better, because it means that the flow is closer to a laminar flow, hence less pressure loss. If your value hits between two lines it is advised to pick the top line to be on the safe side. It is always better to assume worse constitutions and to buy a stronger pump than your fluids not transferring.

The d/k ratio is the y axis and Reynolds number is the x axis. use this Moody chart. Find your intersection point with the horizontal lines and see what is your λ factor.

E.g. for d=30mm, k=0.003mm and Re=10^{6}

λ = 0.0135

Sum the ζ values (resistivity number). Note that some questions will note the ζ value just once although there are multiple valves. You need to multiple the value by the number of valves.

You are almost done, just enter the λ factor, the pipe length and diameter, ζ sum, density and linear velocity to the equation above.

Endnote

I would recommend to calculate each part separately and sum it, because it reduce the chance of you to enter something wrong into your calculator. Be aware that ∆P_{p} and ∆P_{s} can have negative value. Which is good because that means that you need less powerful pump to transfer your liquids. That occurs when your source tank is higher than your target tank and or has higher pressure. If the end value is negative you do not need a pump to transfer your liquids!

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