【正文】 icating liquid is mercury. The top of the manometer is filled with the water to prevent from the mercury vapor diffusing into the air, and the height R3=50mm. Try to calculate the pressure at point A and B. Figure for problem Solution: There is a gaseous mixture in the Utube manometer meter. The densities of fluids are denoted by , respectively. The pressure at point A is given by hydrostatic equilibrium is small and negligible in parison withand ρH2O , equation above can be simplified= =1000+13600=7161N/m178。=7161+13600=60527N/mDdpapaHhAFigure for problem Water discharges from the reservoir through the drainpipe, which the throat diameter is d. The ratio of D to d equals . The vertical distance h between the tank A and axis of the drainpipe is 2m. What height H from the centerline of the drainpipe to the water level in reservoir is required for drawing the water from the tank A to the throat of the pipe? Assume that fluid flow is a potential flow. The reservoir, tank A and the exit of drainpipe are all open to air.Solution:Bernoulli equation is written between stations 11 and 22, with station 22 being reference plane:Where p1=0, p2=0, and u1=0, simplification of the equation 1The relationship between the velocity at outlet and velocity uo at throat can be derived by the continuity equation: 2Bernoulli equation is written between the throat and the station 22 3Combining equation 1,2,and 3 givesSolving for HH= A liquid with a constant density ρ kg/m3 is flowing at an unknown velocity V1 m/s through a horizontal pipe of crosssectional area A1 m2 at a pressure p1 N/m2, and then it passes to a section of the pipe in which the area is reduced gradually to A2 m2 and the pressure is p2. Assuming no friction losses, calculate the velocities V1 and V2 if the pressure difference (p1 p2) is measured.Solution: In , the flow diagram is shown with pressure taps to measure p1 and p2. From the massbalance continuity equation , for constant ρ where ρ1 = ρ2 = ρ,For the items in the Bernoulli equation , for a horizontal pipe,z1=z2=0Then Bernoulli equation bees, after substituting for V2,Rearranging,Performing the same derivation but in terms of V2, A liquid whose coefficient of viscosity is 181。 dB=zAzB=l=Q= m3/s,pBpA=14715 N/m2When the fluid flows down, writing mechanical balance equationmaking the static equilibriumFigure for problem ．The liquid vertically flows down through the tube from the station a to the station b, then horizontally through the tube from the station c to the station d, as shown in figure. Two segments of the tube, both ab and cd，have the same length, the diameter and roughness.Find:（1）the expressions of , hfab, and hfcd, respectively.（2）the relationship between readings R1and R2 in the U tube.Solution:(1) From Fanning equationandsoFluid flows from station a to station b, mechanical energy conservation gives hence 2from station c to station dhence 3From static equationpapb=R1（ρˊρ）g lρg 4pcpd=R2（ρˊρ）g 5Substituting equation 4 in equation 2 ，thentherefore 6Substituting equation 5 in equation 3 ，then 7ThusR1=R2 Water passes through a pipe of diameter di= m with the average velocity m/s, as shown in Figure. 1) What is the pressure drop –DP when water flows through the pipe length L=2 m, in m H2O column?LrFigure for problem 2) Find the maximum velocity and point r at which it occurs. 3) Find the point r at which the average velocity equals the local velocity.4）if kerosene flows through this pipe，how do the variables above change？（the viscosity and density of Water are Pas and 1000 kg/m3，respectively；and the viscosity and density of kerosene are Pas and 800 kg/m3，respectively）solution:1） from HagenPoiseuille equation2）maximum velocity occurs at the center of pipe, from equation so umax=2=3）when u=V=4) kerosene: As shown in the figure, the water level in the reservoir keeps constant. A steel drainpipe (with the inside diameter of 100mm) is connected to the bottom of the reservoir. One arm of the Utube manometer is connected to the drainpipe at the position 15m away from the bottom of the reservoir, and the other is opened to the air, the U tube is filled with mercury and the leftside arm of the U tube above the mercury is filled with water. The distance between the upstream tap and the outlet of the pipeline is 20m. a) When the gate valve is closed, R=600mm, h=1500mm。/h)b) When the gate valve is widely open, calculate the static pressure at the tap (in gauge pressure, N/m178。then （c）since input the above data into equation c， the velocity is: V= m/sWrite mechanical energy balance equation between thestations 1—1’ and 2——2’, for the same situation of water level （d）since input the above data into equation d， =the pressure is: Water at 20℃ passes through a steel pipe with an inside diameter of 300mm and 2m long. There is a attachedpipe (Φ60180。/h 26Total heads，m Shaft power ，kW Efficiency ，% Water is transported by a pump from reactor, which has 200 mm Hg vacuum, to the tank, in which the gauge pressure is kgf/cm2, as shown in Fig. The total equivalent length of pipe is 200 m including all local frictional loss. The pipeline is f57 mm , the orifice coefficient of Co and orifice diameter do are and 25 mm, respectively. Frictional coefficient l is . Calculate: Developed head H of pump, in m (the reading R of U