【正文】 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。). 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。 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。 flows below the critical velocity for laminar flow in a circular pipe of diameter d and with mean velocity V. Show that the pressure loss in a length of pipe is .Oil of viscosity Pas flows through a pipe of diameter with a average velocity of Solution:The average velocity V for a cross section is found by summing up all the velocities over the cross section and dividing by the crosssectional area 1From velocity profile equation for laminar flow 2substituting equation 2 for u into equation 1 and integrating 3rearranging equation 3 givesFigure for problem . In a vertical pipe carrying water, pressure gauges are inserted at points A and B where the pipe diameters are and respectively. The point B is below A and when the flow rate down the pipe is m3/s, the pressure at B is 14715 N/m2 greater than that at A. Assuming the losses in the pipe between A and B can be expressed as where V is the velocity at A, find the value of k.If the gauges at A and B are replaced by tubes filled with water and connected to a Utube containing mercury of relative density , give a sketch showing how the levels in the two limbs of the Utube differ and calculate the value of this difference in metres. Solution: dA=。 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 ind