【正文】 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。 when the gate valve is opened partly, R=400mm, h=1400mm. The friction coefficient λ is , and the loss coefficient of the entrance is . Calculate the flow rate of water when the gate valve is opened partly. (in m179。/h)b) When the gate valve is widely open, calculate the static pressure at the tap (in gauge pressure, N/m178。). le/d≈15 when the gate valve is widely open, and the friction coefficient λ is still .Figure for problem Solution：(1) When the gate valve is opened partially, the water discharge is Set up Bernoulli equation between the surface of reservoir 1—1’ and the section of pressure point 2—2’，and take the center of section 2—2’ as the referring plane, then （a）In the equation (the gauge pressure) When the gate valve is fully closed, the height of water level in the reservoir can be related to h (the distance between the center of pipe and the meniscus of left arm of U tube). （b） where h=R=Substitute the known variables into equation b Substitute the known variables equation a =the velocity is V = the flow rate of water is 2） the pressure of the point where pressure is measured when the gate valve is wideopen. Write mechanical energy balance equation between the stations 1—1’ and 33180。，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。) which is parallel with the main pipe. The total length including the equivalent length of all form losses of the attachedpipe is 10m. A rotameter is installed in the branch pipe. When the reading of the rotameter is , try to calculate the flow rate in the main pipe and the total flow rate, respectively. The frictional coefficient of the main pipe and the attachedpipe is and , respectively.Solution： The variables of main pipe are denoted by a subscript1, and branch pipe by subscript 2. The friction loss for parallel pipelines is The energy loss in the branch pipe is In the equation input the data into equation c The energy loss in the main pipe is So The water discharge of main pipe is Total water discharge is A Venturimeter is used for measuring flow of water along a pipe. The diameter of the Venturi throat is two fifths the diameter of the pipe. The inlet and throat are connected by water filled tubes to a mercury Utube manometer. The velocity of flow along the pipe is found to be m/s, where R is the manometer reading in metres of mercury. Determine the loss of head between inlet and throat of the Venturi when R is . (Relative density of mercury is ).Figure for problem Solution:Writing mechanical energy balance equation between the inlet 1 and throat o for Venturi meter 1rearranging the equation above, and set (z2z1)=x 2from continuity equation 3substituting equation 3 for Vo into equation 2 gives 4from the hydrostatic equilibrium for manometer 5substituting equation 5 for pressure difference into equation 4 obtains 6rearranging equation 6 acid of specific gravity is flowing through a pipe of 50 mm internal diameter. A thinlipped orifice, 10mm, is fitted in the pipe and the differential pressure shown by a mercury manometer is 10cm. Assuming that the leads to the manometer are filled with the acid, calculate (a)the weight of acid flowing per second, and (b) the approximate friction loss in pressure caused by the orifice.The coefficient of the orifice may be taken as , the specific gravity of mercury as , and the density of water as 1000 kg/m3Solution:a)b) approximate pressure droppressure difference due to increase of velocity in passing through the orifice pressure drop caused by friction loss Water is used to test for the performances of pump. The gauge pressure at