Concept explainers
Water flows at mass flow rate m through a 90° vertically oriented elbow of elbow radius R (to the centerline) and lime, pipe diameter D as sketched. The outlet s exposed to the atmospheric. (Hint: This means that the pressure at the outlet is atmospheric pressure.) The pressure at the inlet must obviously be higher than atmospheric in order to push the water through the elbow and to raise the elevation of the water. The irreversible head loss through the elbow is hL. Assume that the kinetic energy flux correction factor a is not unity, but is the same at the inlet and outlet of the elbow
(a) Using the head form of the energy equation, derive an expression for the gage pressure
(b) Plug in these numbers and solve for
(c) Neglecting the weight of the elbow itself and the weight of the water in the elbow, calculator the x and z components of the anchoring force required to hold the elbow in place. Your final answer for the anchoring force should be given as a
(d) Repeat Part (c) without neglecting the weight of the water in the elbow. Is it reasonable to neglect the weight of the water in this problem?
(a)
The expression of gage pressure using the head form of energy equation.
Answer to Problem 96P
The expression of gage pressure is
Explanation of Solution
Given information:
The elbow is
Write the expression of Bernoullis equation at inlet and outlet of elbow pipe.
Here, the pressure at inlet is
Write the expression of gage pressure.
Here, the inlet pressure is
Consider, the velocity of flow at inlet and outlet is same i.e.
Substitute,
Substitute
Conclusion:
The expression of gage pressure is
(b)
The gage pressure.
Answer to Problem 96P
The gage pressure is
Explanation of Solution
Given information:
The density of the fluid is
Calculation:
Substitute
Conclusion:
The gage pressure is
(c)
The
Answer to Problem 96P
The
The
Explanation of Solution
Given information:
Neglect the weight of elbow and weight of the water.
Write the expression of
Here, the momentum flux correction factor is
Substitute,
Write the expression of
Here, the momentum flux correction factor is
Substitute
Write the expression of mass flow rate of fluid.
Here, the density of the fluid is
Write the expression of area of flow.
Here, the diameter of the pipe is
Calculation:
Substitute
Substitute
Substitute
So, the force is acting on opposite direction.
Substitute
Conclusion:
The
The
(d)
The
Answer to Problem 96P
The
The
Explanation of Solution
Given information:
The weight of water in the elbow is considered.
Write the expression of
Here, the momentum flux correction factor is
Substitute,
Write the expression of
Here, the momentum flux correction factor is
Substitute
Write the expression of weight of water in the elbow.
Here, the mass of water is
Write the expression of mass of water.
Here, the density of the fluid is
Write the expression of volume of water.
Here, the area of flow is
Calculation:
Substitute
So, the force is acting on opposite direction.
Substitute
Substitute
Substitute
Substitute
Conclusion:
The
The
Want to see more full solutions like this?
Chapter 6 Solutions
Fluid Mechanics: Fundamentals and Applications
- Water is flowing steadily through a closed pipe system of constant diameter. Station 2 is 1 m higher than Station 1. At Station 1, the average speed of the water is 3 m/s. If the static pressure at Station 1 is 20 kPa, what is the static pressure at Station 2? Hint: If the cross sectional pipe areas at station 1 and 2 are the same, then the velocity at both stations must.. Select one: O a. 6.69 kPa O b. 10.19 kPa O c. 22.69 kPa O d. 10.19 kN Next page page OSearch for anythingarrow_forwardAs seen in the figure above, the water is directed downward in the installation with a 25 ° angle narrowing elbow in a piping system with a volumetric flow of 0.025 m3 / s. Effective pressure at 1 point is measured as 2 bar. Where the flow is frictionless and gravitational effects are neglected(a) Calculate the effective (effective) pressure at point 2(b) Calculate the x and y components of the force required to hold the elbow in place and the resultant force (water = 1000 kg / m3, g = 9.81 m / s2).arrow_forwardThe diameters Dº & dº piped, Venturi- meter like horizontal water flow sistem seen in the drawing is connected to a piston - cylinder system of DPⓇ piston and dp rod diameter and connected to the incoming flow pipe and the cont- racted cross section. Assuming that the ideal - no head loss flow conditions are valid ; Calculate the force F applied to the pis- ton when the average velocity and the pressure at the entrance cross-section is V and p' respectively. Dº = 10 [mm] dº = 5 [mm] " & D dp p* V -FD₂ p = 4,5 [bar] Dp = 30 [mm] dº Pw Horizontal Setup V = 5 [m/s] dp = 6 [mm]arrow_forward
- A centrifugal pump having a head-capacityrelationship given by the equation ha=180 –6.10 X 10-4 Q2, with ha in feet when Q is ingpm, is to be used with the system shownin the figure, For Z2-Z1= 50 ft, what is theexpected flowrate if the total length ofconstant diameter pipe is 600 ft and thefluid is water? Assume the pipe diameter tobe 4 inch and the friction factor to be equalto 0.02. Neglect all minor losses.arrow_forwardA four-stage centrifugal pump has four identical impellers, keyed to the same shaft. The shaft is running at 400 r.p.m. and the total manometric head developed by the multistage pump is 40m. The discharge through the pump is 0.2 m*3/s. The vanes of each impeller are having outlet angle as 45°. If the width and diameter of each impeller at outlet is 5cm and 60 cm respectively, Find the manometric efficiency.arrow_forward(c) The above pump is scaled up to 46 cm diameter operating in water at BEP at 1760 rev/min. The measured NPSH is 4.88 m and the friction loss between the inlet and pump is 6.71 m. Will it be sufficient to avoid cavitation if the pump inlet is placed 2.74 m below the surface of a sea level reservoir? The barometric pressure is 740 mm Hg and the vapour pressure of water at the prevailing temperature is 26 mm Hg. The specific gravity of Hg is 13.55. (d) A 70 cm diameter centrifugal pump which is dynamically similar to the tested pump tabulated above, is delivering water at 1.26 m³/s against a 100m head. Determine the operating speed in rev/min and the required power consumption. Note that the pump is not necessarily running at the design point. Use SI system for your calculations where the pump speed N should be in rad/sec. You may take density of water as 1000 kg/m³ and standard acceleration of gravity g = 9.81 m/s².arrow_forward
- Problem 4: For the siphon in the figure below, calculate (a) the volume flow rate of water through the nozzle and (b) the pressure at points A and B. The distances X = 4.6 m and Y = 0.90 m. 早 Water 50-mm OD X 1.5-mm wall 25-mm diameter 6,838 3141603 FEB 28 rw 吕0 00arrow_forwardIn a pipe of diameter 300mm the center line velocity and the velocity at a point 100mm from the center, as measured by pitot tube are 2.4 m/s and 2.0 m/s respectively. Assume the flow in the pipe to be turbulent find: 1-Dischrge through the pipe,2-Coefficient of friction, 3 Height of roughness projections.Please do not waste my question solve with correct answers only.arrow_forwardA pump is needed to drain an excavation at a construction site. The excavation has alength of 50m, width of 50m, and a depth of 4m. The surface of the water in the excavation lies at adepth, H=3m, from the top the of the excavation. An old, radial flow, 1000W pump is immediatelyavailable for use; however, the total pump-motor efficiency, e, is only 50%. Estimate the drawdown inthe excavation in the first 4 hours of pumping. Neglect the change in H with increasing time. Neglectany head loss in the hose/pipe connected to the pump. (Hint: utilize the Pout equation, consider analternative definition of discharge as a change in volume over a change in time). Assume a specificweight of 9.79kN/m 3 .arrow_forward
- The below figure shows a pump that transfers a steady stream of 35◦API crude oil from an oiltanker to a refinery storage tank, both free surfaces being open to the atmosphere. Theeffective length—including fittings—of the commercial steel pipe is 6,000 ft. The dischargeat point 4 is 200 ft above the pump exit, which is level with the free surface of oil in thetanker. However, because of an intervening hill, point 3 is at a higher altitude than point 4.Losses between points 1 and 2 may be ignored.The crude oil has the following properties:Density ρ = 53 lbm/ft 3 ; Viscosity μ = 13.2 cP; Vapour Pressure Pv = 4.0 psia Answer the following questions:1. If the combination of pump and motor is 80% efficient, how much electrical power(kW) is needed to drive the pump?2. If, in order to avoid vapour lock, the pressure in the pipeline must always be above thevapor pressure of the crude oil, what is the maximum permissible elevation of point 3relative to point 4?3. If the flow in the pipeline…arrow_forwardAa certain hydro-power station has a head of 500m between the upper and lower reservior. A. Determing the approach velocity of water as it enters the turbine ; B. If the volume flowrate is 60cumec, what is the diameter of the penstock; and C. If the head loss due to friction represents 10% of the static head in (a) determine the actual velocity approach and the corrected diameter of the penstock requiredarrow_forwardAir at 110°F passes through a -in-diameter orifice having a flow capacity constant of 3.5. If the upstream pressure is 1500 psi, what is the maximum flow rate in units of scfm of air? 2arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY