Answer:
20.87 Pa
Explanation:
The formula for dynamic pressure is given as;
q= 1/2*Ļ*vĀ²
where ;
q=dynamic pressure
Ļ = density of fluid
v = velocity of fluid
First find v by applying the formula for flow rate as;
Q = v*A Ā where ;
Q= fluid flow rate
v = flow velocity
A= cross-sectional area.
A= cross-sectional vector area of the pipe given by the formula;
A= ĻrĀ² = 3.14 * 4Ā² = 50.27 inĀ² Ā where r=radius of pipe obtained from the diameter given divided by 2.
Q = fluid flow rate = 105 gpm----change to mĀ³/s as
1 gpm = 0.00006309
105 gpm = 105 * 0.00006309 = 0.006624 mĀ³/s
A= cross-sectional vector area = 50.27 inĀ² -------change to mĀ² as:
1 inĀ² = 0.0006452 mĀ²
50.27 inĀ² = 50.27 * 0.0006452 = 0.03243 mĀ²
Now calculate flow velocity as;
Q =v * A
Q/A = v
0.006624 mĀ³/s / 0.03243 mĀ² =v
0.2043 m/s = v
Now find the dynamic pressure q given as;
q= 1/2 * Ļ*vĀ²
q= 1/2 * 1000 * 0.2043Ā² = 20.87 Pa
