Chapter 19, Problem 19.1PP

Determine the velocity of flow and the friction loss as $1000$ cfm of air flows through $75$ ft of an $18$ -in-diameter round duct.

To determine

The velocity of flow

The value of friction loss

Answer to Problem 19.1PP

The velocity of flow, V=570ft/min

The value of friction loss, H_L=0.021 in H₂O

Explanation of Solution

Given information:

Diameter of the duct, D=18in

Rate of flow, Q=1000 cfm

Length of the duct, L=75 ft

To find out the friction loss, we use the formula

   $H_L=h_L.(\frac{L}{100})\mathrm{............................................}(1)$

Where,

L= Length of the duct

H_L=Friction loss

h_L=friction loss of water per 100 ft

friction loss of water per 100 ft is calculated by the chart of friction loss in a duct and it is equal to h_L=0.028 in H₂O

We compare between any two given values and their intersecting point give the third required value

The velocity of flow is also calculated by the chart of friction loss in a duct and it is equal to

The V=570ft/min

Calculation:

Now we put the known values in equation

   $\begin{array}{l}{H}_L=h_L.(\frac{L}{100})\\ H_L=(0.028)X\frac{75}{100}\end{array}$

H_L= 0.021 in H₂O