Answer:
(a) The volume rate of flow per meter width = 5.6*10⁻³ m²/s
(b) The shear stress acting on the bottom plate = 157.5 N/m²
(c) The velocity along the centerline of the channel = 0.93 m/s
Explanation:
(a)
Calculating the distance of plate from centre line using the formula;
h = d/2
where h = distance of plate
d = diameter of flow = 9 mm
Substituting, we have;
h = 9/2
= 4.5 mm = 4.5*10^-3 m
Calculating the volume flow rate using the formula;
Q = (2h³/3μ)* (Δp/L)
Where;
Q = volume flow rate
h = distance of plate = 4.5*10^-3 m
μ = dynamic viscosity = 0.38 N.s/m²
(Δp/L) = Pressure drop per unit length = 35 kPa/m = 35000 Pa
Substituting into the equation, we have;
Q = (2*0.0045³/3*0.38) *(35000)
= (1.8225*10⁻⁷/1.14) * (35000)
= 1.60*10⁻⁷ * 35000
= 5.6*10⁻³ m²/s
Therefore, the volume flow rate = 5.6*10⁻³ m³/s
(b) Calculating the shear stress acting at the bottom plate using the formula;
τ = h*(Δp/L)
= 0.0045* 35000
= 157.5 N/m²
(c) Calculating the velocity along the centre of the channel using the formula;
u(max) = h²/2μ)* (Δp/L)
= (0.0045²/2*0.38) * 35000
=2.664*10⁻⁵ *35000
= 0.93 m/s
