An annulus of narrow clearance causes a large pressure drop and can be used to measure fluid viscosity accurately. A smooth annulus has:L=1.0 m,a=50 mm,b=49 mmOil flows through the annulus at Q=2.00×10−3 m3/s If the measured pressure drop isΔp=250 kPa What is the oil viscosity μ in kg/m.s?  

Water at 20∘C20^\circ\text{C} (ρ=998 kg/m3)(\rho = 998\ \text{kg/m}^3) flows through an inclined pipe of diameter 8 cm8\ \text{cm}. At sections AA and BB, the following data are measured: pA=186 kPa,VA=3.2 m/s,zA=22.50 mp_A = 186\ \text{kPa}, \quad V_A = 3.2\ \text{m/s}, \quad z_A = 22.50\ \text{m}pB=260 kPa,VB=3.2 m/s,zB=9.1 m   Determine the head loss hfh_f​ for the flow in m.

Heat exchangers often consist of many triangular passages. Consider the triangular duct shown in the figure with:   L=78.0 cm,a=2.0 cm, β=80∘L = 52.0\ \text{cm}, \qquad a = 2.0\ \text{cm}, \qquad \beta = 80^\circT The average fluid velocity isV=2.0 m/sV = 2.0\ \text{m/s} The fluid is SAE 10 oil at 20∘C20^\circ\text{C}, with properties ρ=870 kg/m3,μ=0.104 kg/(m.s)\rho = 870\ \text{kg/m}^3, \qquad \mu = 0.104\ \text{kg/(m\cdot s)} Estimate the pressure drop Δp\Delta p in Pa through the triangular passage.      

Water at 20∘C20^\circ\text{C} is pumped through a pipe connecting two reservoirs at a flow rate: Q=3 ft3/sQ = 3\ \text{ft}^3/\text{s}Pipe data: L=2700 ft,D=6 inL = 2100\ \text{ft}, \quad D = 6\ \text{in}Elevation difference: Δz=120 ft\Delta z = 120\ \text{ft}Pump efficiency: η=75%\eta = 75\% ρ=1.94 slug/ft3,μ=2.09×10−5 slug/(ft.s)\rho = 1.94\ \text{slug/ft}^3, \quad \mu = 2.09\times10^{-5}\ \text{slug/(ft\cdot s)}For cast iron: ε=0.00085 ft What horsepower must the pump supply?  

Water at 20∘C20^\circ\text{C} (ρ=998 kg/m3)(\rho = 998\ \text{kg/m}^3) flows through an inclined pipe of diameter 8 cm8\ \text{cm}. At sections AA and BB, the following data are measured: pA=186 kPa,VA=3.2 m/s,zA=23.50 mp_A = 186\ \text{kPa}, \quad V_A = 3.2\ \text{m/s}, \quad z_A = 23.50\ \text{m}pB=260 kPa,VB=3.2 m/s,zB=9.1 mp_B = 260\ \text{kPa}, \quad V_B = 3.2\ \text{m/s}, \quad z_B = 9.1\ \text{m} Determine the head loss hfh_f​ for the flow.

Flow in a pipe is measured using an orifice plate, as shown in the figure. The volumetric flow rate QQ depends on the pressure drop across the plate Δp\Delta p, fluid density ρ\rho, pipe diameter DD, and orifice diameter dd. Task: Using dimensional analysis, express this relationship in dimensionless form.   Select the correct answer: A. ρQD2=f ⁣(dD)\displaystyle \frac{\rho Q}{D^2} = f\!\left(\frac{d}{D}\right) B. ρQD2Δp=f ⁣(dD)\displaystyle \frac{\rho Q}{D^2 \Delta p} = f\!\left(\frac{d}{D}\right) C. ρQΔp=f ⁣(dD)\displaystyle \frac{\rho Q}{\sqrt{\Delta p}} = f\!\left(\frac{d}{D}\right) D. ρ QD2Δp=f ⁣(dD)\displaystyle \frac{\sqrt{\rho}\,Q}{D^2 \sqrt{\Delta p}} = f\!\left(\frac{d}{D}\right)    

A fixed cylinder of diameter DD and length LL, immersed in a uniform stream of velocity UU flowing normal to its axis, experiences zero average lift when it is not rotating. However, when the cylinder rotates at angular velocity Ω\Omega, a lift force FF is generated.\Omega Neglect viscous effects. Using dimensional analysis, express the lift force relationship in dimensionless form. Select the correct answer: A. FρU2D2=f ⁣(ΩDU,LD)\displaystyle \frac{F}{\rho U^2 D^2}=f\!\left(\frac{\Omega D}{U},\frac{L}{D}\right) B. FρU2D2=f ⁣(ΩρU,ULD)\displaystyle \frac{F}{\rho U^2 D^2}=f\!\left(\frac{\Omega \rho}{U},\frac{UL}{D}\right) C. FρU2D2=f ⁣(ΩD,ULD)\displaystyle \frac{F}{\rho U^2 D^2}=f\!\left(\frac{\Omega}{D},\frac{UL}{D}\right) D. FρU2D2=f ⁣(ΩLU,ρD)\displaystyle \frac{F}{\rho U^2 D^2}=f\!\left(\frac{\Omega L}{U},\frac{\rho}{D}\right)

Heat exchangers often consist of many triangular passages. Consider the triangular duct shown in the figure with: L=52.0 cm,a=2.0 cm,β=80∘L = 52.0\ \text{cm}, \qquad a = 2.0\ \text{cm}, \qquad \beta = 80^\circThe average fluid velocity is V=2.0 m/sV = 2.0\ \text{m/s} The fluid is SAE 10 oil at 20∘C20^\circ\text{C}, with properties ρ=870 kg/m3,μ=0.104 kg/(m.s)\rho = 870\ \text{kg/m}^3, \qquad \mu = 0.104\ \text{kg/(m\cdot s)} Estimate the pressure drop Δp\Delta p in Pa through the triangular passage.      

For the configuration shown in the figure given below, the fluid is ethyl alcohol at 20°C, and the tanks are very wide. The diameter d of the tube is 2.100 mm. Find the flow rate that occurs in m3/h.   

Flow through the converging nozzle shown in the figure is approximated as one-dimensional, with velocity components u(x)=V0(1+2xL), v≈0, w≈0u(x)=V_0\left(1+\frac{2x}{L}\right), \qquad v \approx 0, \qquad w \approx 0 where V0V_0and LL  are constants. Find a general expression for the fluid acceleration in the nozzle. Select the correct answer: A. DuDt=2V0L(1+2xL)\displaystyle \frac{Du}{Dt}=\frac{2V_0}{L}\left(1+\frac{2x}{L}\right) B. DuDt=V0L(1+2xL)\displaystyle \frac{Du}{Dt}=\frac{V_0}{L}\left(1+\frac{2x}{L}\right) C. DuDt=V02L(1+2xL)\displaystyle \frac{Du}{Dt}=\frac{V_0^2}{L}\left(1+\frac{2x}{L}\right) D. DuDt=2V02L(1+2xL)\displaystyle \frac{Du}{Dt}=\frac{2V_0^2}{L}\left(1+\frac{2x}{L}\right)