Answer:
20.87 Pa
Explanation:
The formula for dynamic pressure is given as;
q= 1/2*ρ*v²
where ;
q=dynamic pressure
ρ = density of fluid
v = velocity of fluid
First find v by applying the formula for flow rate as;
Q = v*A 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= πr² = 3.14 * 4² = 50.27 in² where r=radius of pipe obtained from the diameter given divided by 2.
Q = fluid flow rate = 105 gpm----change to m³/s as
1 gpm = 0.00006309
105 gpm = 105 * 0.00006309 = 0.006624 m³/s
A= cross-sectional vector area = 50.27 in² -------change to m² as:
1 in² = 0.0006452 m²
50.27 in² = 50.27 * 0.0006452 = 0.03243 m²
Now calculate flow velocity as;
Q =v * A
Q/A = v
0.006624 m³/s / 0.03243 m² =v
0.2043 m/s = v
Now find the dynamic pressure q given as;
q= 1/2 * ρ*v²
q= 1/2 * 1000 * 0.2043² = 20.87 Pa
