In this post we are going to see how to calculate External Static Pressure (ESP), and what is meant by external static pressure (esp)?

**External Static Pressure (ESP) :**

** **External Static Pressure is the estimation of all the obstruction in the channel framework, that the fan needs to neutralize. Some of the examples are grills, filters, Air conditioning coils, and the ventilation duct work. It is the amount of the pull pressure (negative) and release pressure (positive) made by the hardware blower. External Static Pressure is estimated utilizing a manometer and is expressed in inch of water column. i.e; (**"WC**).

Next, we will see how to calculate the external static pressure with an example.

**Example :**

** *** Calculate the external static pressure for the following data :

Length of duct = 23 m

Size of the duct = 600 x 400 for 8 m length, 500 x 300 for 8 m length and 400 x 250 for 7 m length.

Calculate the external static pressure required for the above given data. Consider velocity 1500 fpm and constant C = 1.25

Let us see the solution for the above example.

**Solution :**

First step is to find the equivalent diameters of all three given duct sizes. Equivalent diameters can be easily found from a software named **"Mcquay Duct Sizer " **, by simply entering the duct sizes. As i have calculated for three duct sizes you can see below.

For Duct Size 600 x 400, Equivalent diameter D = 20

For Duct Size 500 x 300, D = 18.8

For Duct Size 400 x 250, D = 13.8

The first step is to calculate the friction loss, the formula for friction loss is :

**Friction Loss = (L/D) x 0.0195 x Vp**

where L is the Length of Duct,

D is the equivalent diameter of that duct,

and Vp is the Velocity Pressure.

Next we have to find the Dynamic Loss. The formula for Dynamic loss is :

**Dynamic Loss = Dynamic Loss Coefficient x Vp**

Vp can be easily calculated by using this formula :

**Vp = (Velocity/ 4005)****²**

Next, Let us insert the Velocity value 1500 fpm in the Vp formula

Vp = ( 1500/ 4005)²

therefore, Vp = 0.14027

Now, Let us see some conversions.

As we all know, 1 metre = 3.28 ft and metre to --- ft to --- inches = length x 3.28 x 12

Now, let us find out the external static pressure for three different duct sizes and finally add them together to get the final static pressure.

**(1) For Duct Size 600 x 400 :**

Friction Loss = (L/D) x 0.0195 x Vp

Let us substitute the values from the given data in the above formula and we get

Friction Loss = (8 x 3.28 x 12 / 20) x 0.0195 x 0.14027

= 0.043 water inch / 100 ft

which is the friction loss for 600 x 400 duct size. Now we will calculate the dynamic loss for the same.

Dynamic Loss = Dynamic Loss Coefficient x Vp

= 1.25 x 0.14027 (Here dynamic loss coefficient C is a constant , C = 1.25 )

therefore, Dynamic Loss = 0.17533 water inch / 100 ft

Next let us calculate similarly for second duct size which is 500 x 300.

**(2) For Duct Size 500 x 300 :**

Friction Loss = (L/D) x 0.0195 x Vp

Let us substitute the values from the given data in the above formula and we get

Friction Loss = (8 x 3.28 x 12 / 18.8) x 0.0195 x 0.14027

= 0.046 water inch / 100 ft

which is the friction loss for 500 x 300 duct size. Now we will calculate the dynamic loss for the same.

Dynamic Loss = Dynamic Loss Coefficient x Vp

= 1.25 x 0.14027 (Here dynamic loss coefficient C is a constant , C = 1.25 )

therefore, Dynamic Loss = 0.17533 water inch / 100 ft

Next we will calculate for the third duct size, which is 400 x 250

**(2) For Duct Size 400 x 250 :**

Friction Loss = (L/D) x 0.0195 x Vp

Let us substitute the values from the given data in the above formula and we get

Friction Loss = (7 x 3.28 x 12 / 13.8) x 0.0195 x 0.14027

= 0.054 water inch / 100 ft

which is the friction loss for 400 x 250 duct size. Now we will calculate the dynamic loss for the same.

Dynamic Loss = Dynamic Loss Coefficient x Vp

= 1.25 x 0.14027 (Here dynamic loss coefficient C is a constant , C = 1.25 )

therefore, Dynamic Loss = 0.17533 water inch / 100 ft

Now we got, friction loss , dynamic loss, for three duct sizes. Next, we will add all three dynamic losses from three duct sizes.

Dynamic Loss = 0.175 + 0.175 + 0.175

All dynamic losses are same, since the coefficient is 1.25

therefore, Total Dynamic Loss = 0.525 water inch / 100 ft

Add friction losses of all three ducts as well

Friction Loss = 0.043 + 0.046 + 0.054

therefore, Total Friction Loss = 0.143 water inch / 100 ft

Next, we will add the total dynamic loss and friction loss, in order to get the Total External Static Pressure.

**Duct Static Pressure (ESP) = **0.143 + 0.525

therefore, **ESP = 0.668 water inch / 100 ft**

We need to convert this water inch / 100 ft into Pascal. So, multiply the result by 250.

So, **ESP = 0.668 x 250**

**Therefore, Esp (External Static Pressure ) **= 167 Pa.

**Note : **Important point to be noted here is, This is only the external static pressure for ducts of different sizes. For remaining Accessories that come inside the duct, like filters, grills, louvers, sound attenuators, etc. you need to get the pressure losses from the respective supplier and add it to this calculated ESP, in order to get the final pressure loss.

Hope this article is a bit helpful in letting you know, how to calculate the external static pressure or esp. Keep learning.. Keep Growing..

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