【正文】 om 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。 A differential manometer as shown in Fig. is sometimes used to measure small pressure difference. When the reading is zero, the levels in two reservoirs are equal. Assume that fluid B is methane（甲烷）, that liquid C in the reservoirs is kerosene (specific gravity = ), and that liquid A in the U tube is water. The inside diameters of the reservoirs and U tube are 51mm and , respectively. If the reading of the manometer is145mm., what is the pressure difference over the instrument In meters of water, (a) when the change in the level in the reservoirs is neglected, (b) when the change in the levels in the reservoirs is taken into account? What is the percent error in the answer to the part (a)? Solution：pa=1000kg/m3 pc=815kg/m3 pb=When the pressure difference between two reservoirs is increased, the volumetric changes in the reservoirs and U tubes (1)so (2)and hydrostatic equilibrium gives following relationship (3)so (4)substituting the equation (2) for x into equation (4) gives (5)（a）when the change in the level in the reservoirs is neglected, （b）when the change in the levels in the reservoirs is taken into accounterror= There are two Utube manometers fixed on the fluid bed reactor, as shown in the figure. The readings of two Utube manometers are R1=400mm，R2=50mm, respectively. The indicating 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。 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。) 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 the discharge connection is 152 kPa and the reading of vacuum gauge at the suction connection of the pump is kPa as the flow rate is 26m3/h. The shaft power is while the centrifugal pump operates at the speed of 2900r/min. If the vertical distance between the suction connection and discharge connection is , the diameters of both the suction and discharge line are the same. Calculate the mechanical efficiency of pump and list the performance of the pump under this operating condition.Solution: Write the mechanical energy balance equation between the suction connection and discharge connection wheretotal heads of pump is efficiency of pump is since N=Then mechanical efficiency The performance of pump is Flow rate ，m179。=103Ns/m2 so 1from the maximum permissible velocity of the air is 3m/s 2set B to be 3m, then from equation 1L=7mAnd H= A standard cycl