What is the pressure drop in pipe

When a fluid flows through a pipe, it doesn’t maintain the same pressure; the pressure decreases from upstream to downstream. This is majorly due to frictional loss and loss due to elevation changes.

When there is a flow in a pipe, there is friction between adjacent layers of fluid and between the water molecules and the pipe wall. This friction causes a loss of energy, as pressure and velocity energy are partly converted into heat. This is called the pressure drop due to friction or head loss due to friction.

As fluid flows through a piping system with changes in elevation, the pressure at any point is influenced by the height of the fluid above it. In a vertical pipe, when fluid flows upward, the pressure decreases with height because there’s less fluid above exerting downward force. Conversely, at lower points in the pipe, the pressure increases due to the greater weight of fluid pressing down from above. Simply put, pressure drops as fluid rises and increases as fluid falls, due to the effect of gravity on the fluid column. This is called the pressure drop due to elevation change.

Why is pressure drop important?

Pressure drop in piping is very important for engineers because if the pressure drop is too high, pumps or compressors must work harder, leading to more energy use and higher expenses. If the pressure falls below the level needed by the system, the process may not function properly. On the other hand, very low pressure drop usually means oversized pipes and a higher installation cost. That’s why engineers must carefully balance pressure drop with pipe sizing to ensure the system gets the required flow at the right pressure reliably and cost-effectively.

Calculate pressure drop Due to friction

The amount of pressure drop due to friction depends upon

• Flow rate
• Properties of water (specific gravity and viscosity)
• Pipe diameter
• Pipe length,
• Internal roughness of the pipe.

h_{f}= \frac{fLv^2}{2gD}

Pressure drop calculation step by step with example

We will calculate the pressure drop for the configuration below figure. Certain fluid conditions should be given or taken from the necessary project documents before proceeding with the calculations. For the above calculation, the given conditions are as follows.

𝜌 = density of fluid (Kg/m3) @ temprature = 860

D= inner diameter of pipe work (m) = 0. 0971804 ( ID for 4” sch 80 pipe)   

𝜇= Dynamic viscocity of fluid (Ns/m2) = 0.02752 (Read the article for more on viscocity)

Ɛ= Absolute roughness for pipe (m) = 0.000457 ( Take from Fig-2 below or any published paper)

Q= flowrate (m3/hr) = 45.425

𝐿1 = Total length of pipe work (m) = L1 = 11.55 ( calculated from isometrics)

STEP-1: Calculate the velocity of the fluid

A=\frac{𝜋}{4}*𝐷^{2}=\frac{𝜋}{4}*0.0972^{2}=0.0074

Calculate velocity of fluid (m/s)

v=\frac{Q}{A}=\frac{45.425}{0.0074}=1.70

STEP-2: Calculate Reynold’s no

Re=\frac{𝜌𝑉𝐷}{𝜇}=\frac{860*1.70*0.0972}{0.02752}=5166

STEP-3: Categorize the flow

STEP-4: Calculate friction factor

STEP-4a: Calculate friction factor if laminar flow per step 3

𝑓=\frac{64}{Re}

STEP-4b: Calculate friction factor if transition or turbulent flow per step 3

Calculate relative roughness of pipe per below and enter the Moody’s diagram in Fig 3 with relative roughness and the Reynold’s number (to get friction factor as shown in yellow mark.

\text{Relative  roughness}=\frac{Ɛ}{D}=\frac{0.000457}{0.0972}=0.00047

Click here for Moody’s diagram

For our case, with a relative pipe roughness of 0.00047 (≈ 0.005) and a Reynolds number of 5166, the friction factor obtained from Moody’s diagram is 0.026 per yellow mark in above figure.

so 𝑓=0.026

STEP-4c: Calculate friction factor more precisely for transition or turbulent flow per step 3

The Colebrook equation is usually used to get an accurate value of the friction factor. In step 4b, we are using the Moody’s diagram to pick an approximate friction factor value, which we will then use as the initial guess for solving the Colebrook equation.

We will use the Implicit Colebrook equation to get the value of the friction factor. A certain no of iterative trial and error procedures to be done so that the left-hand side value becomes approximately equal to the right-hand side.

\text{colebrook equation}= \frac{1}{(√𝑓)} = -2log10(  (\frac{Ɛ/D}{3.7})+(\frac{2.51}{𝑅𝑒√𝑓}))

Enter this formula in an Excel where you have a left-hand side value and a right-hand side value. Start with the friction factor you get from Moody’s diagram step 4b, which in our case is 0.026. Then in Excel, increase or decrease this value until the left-hand side value and the right-hand side value become approximately equal. See the image below for reference, where we get approximately equal values at 0.037, which is our final friction factor value.

STEP-5: Calculate the length of piping adding the equivalent length for fittings

In a piping system, there are pipes and other components like fittings and valves. When we calculate pressure drop from one point to another, we know the portion of straight pipe used, so we add that up, but what about the fittings? They will also have some pressure drop according to their geometry, right?

So for the fittings, we can use the equivalent length. The Equivalent Length of a pipe fitting is the length of pipe of the same size as the fitting that would give rise to the same pressure drop as the fitting. It has been observed through experiments that if you take this equivalent length (Le) for a fitting and divide it by the pipe diameter (D), the ratio Le/D stays almost the same for all sizes of that fitting. There are published sources that give the value of the (Le/D) ratio for most of the fitting types. So if we know the D (size or ID of the fittings), we can know the equivalent length for it. Two such (Le/D) ratio table is given below in Fig 5 & 6, and we will use that.

𝐿= Total length of pipe work (m) = L1 (length of straight pipe) +L2 (equivalent length for all fittings added)

STEP-5a: Calculate equivalent length of pipe fittings ( elbow)

\text{equivalent length for elbow(m)}=\frac{Le}{D}=13 

Le=13 * 0. 0971804 =1.26  \text{;for 6 elbows i.e 7.58 m} 

STEP-5b: Calculate equivalent length of pipe fittings ( Gate valve)

\text{equivalent length for gate valve(m)}=\frac{Le}{D}=7.5 

Le=7.5* 0. 0971804 =0.73  \text{;for 2 gate valves i.e 1.46 m} 

STEP-5c: Calculate equivalent length of pipe fittings ( Swing check valves)

\text{equivalent length for Swing check valves (m)}=\frac{Le}{D}=95 

Le=95* 0. 0971804 =9.23

Adding them all the total length to be considered for pressure drop we get is

𝐿= Total length of pipe work (m) = L1 (length of straight pipe 11.55 ) + L2 (total equivalent length of pipe work for fittings 7.58 + 1.46 +9.23 ) =29.82 mtr

STEP 6: Calculate pressure drop due to friction from Darcy-Weisbach equation

h_{f}= \frac{fLv^2}{2gD}

h_{f}= \frac{0.037*29.82*1.70^2}{2*9.81*0. 0971804}=1.675 mtr

so the pressure drop due to friction is 1.675 mtr of fluid, and the same can be converted into other units of pressure

(1.675mtr) or ((1.675(𝜌g))=14131pa) or 0.144 kg/cm^2

Calculate pressure drop due to elevation change

This is calculated from below equation:

 \text{pressure drop due to elevation change}    \text{ }P= 𝜌 g h

 P= 860 * 9.8 *  0.5 = 4214pa

in our problem the flow is going downhill towards the vessel so, there will be an increase or gain in pressure.

Total pressure drop

The total pressure drop in a piping system is the combined effect of friction losses and elevation changes. It can be expressed in two equivalent ways depending on how elevation affects the flow direction:

Total pressure drop = pressure drop due to friction + pressure drop due to elevation

or

Total pressure drop = pressure drop due to friction – pressure gain due to elevation

Total pressure drop = 14131 -4214 =9917pa = 0.101 kg/cm2

Alternatively, the same can be calculated in terms of head loss (metres of fluid):

Total Pressure Drop=1.675−0.5=1.175mtr of fluid

which in terms of Pressure is=1.175×860×9.81=9902Pa=0.100kg/cm2