Question 3:
A dye suction device is arranged, as shown in Figure 3. The volumetric flow rate of air through the main
pipe at circular cross-section (1) is given as $Q = 0.0164 \text{ m}^3/\text{s}$ and the volumetric flow rate of the dye which is
sucked from resorvoir A is given as $Q = 0.00082 \text{ m}^3/\text{s}$. The air and the dye flow is mixed in the main pipe
and the mixture flow is then sprayed into a material to be dyed at cross-section (3). The pressure at point B
where the sucked dye enters into main pipe is given as $0.95P_2$ and the diameter of the suction pipe which
connects the reservoir A to the main pipe is $D_1= 1 \text{ cm}$. Determine the manometric (gauge) pressure of
reservoir A, $P_A$ and the density of the mixture flow, $\rho_r$ at section (3). The fluids are incompressible and the
friction can be neglected. The pressure at Sections (1) and (3) in the main pipe is assumed to be atmospheric
except Section (2) and any variation of the velocity over the pipe cross section can be neglected.
The diameter of the cross-section (1), $D_1=10 \text{ cm}$, the diameter of the cross-section (2), $D_2= 5 \text{ cm}$, the
diameter of the cross-section (3), $D_3= 10 \text{ cm}$, the dye density, $\rho_b= 800 \text{ kg/}m^3$ and air density, $\rho_{air} = 1.2 \text{ kg/}m^3$.
The value of gravitational acceleration, g is 9.81 N/kg. (30 Points)
