Water is flowing into and discharging from a pipe U-section as shown in Fig. P6-77. At flange (1). the total absolute pressure is 200 kPa. and 55 kgs flows into the pipe. At flange (2), the total pressure is 150 kPa. At location (3). 15 kg/s of water discharges to the atmosphere, which is at 100 kPa. Detenume the total x- and z-forces at the two flanges connecting the pipe. Discuss the significance of gravity force for this problem. Take the inomentiun-flux correction
factor to be 1.03 throughout the pipes.
The forces along x-direction.
The net force along z-direction.
Answer to Problem 77P
The forces along x-direction is
The net force along z-direction is
Explanation of Solution
Given information:
The total absolute pressure at flange
Figure-(1) represents the free body diagram of U tube.
Figure-(1)
Expression for area of pipe,
Here, diameter of pipe is
Expression for velocity of flow,
Here, mass flow rate is
Expression for mass flow rate through pipe
Here, discharge through pipe
Expression for momentum equation in horizontal direction for pipe
Here, reaction force in horizontal direction for pipe
Expression for momentum equation along vertical direction in pipe
Expression for momentum equation in horizontal direction for pipe
Here, reaction force in horizontal direction for pipe
Expression for momentum equation along vertical direction in pipe
Expression for momentum equation along horizontal direction in pipe
Expression for momentum equation along vertical direction for pipe
Here, reaction force in vertical direction for pipe
Expression for net horizontal force,
Expression for net vertical reaction force,
Expression for weight per unit length for pipe
Here, density of water is
Expression for weight per unit length for pipe
Expression for weight for pipe
Expression for net vertical force,
Calculation:
Substitute
Substitute
Substitute
Refer to Table-A-3 "Properties of saturated water" to obtain density of water as
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The forces along x-direction is
The net force along z-direction is
Want to see more full solutions like this?
Chapter 6 Solutions
Fluid Mechanics: Fundamentals and Applications
- A very popular toy on the market several years ago was the water rocket. Water (at 10°C) was loaded into a plastic rocket and pressurized with a hand pump. The rocket was released and would travel a considerable distance in the air. Assume that a water rocket has a mass of 50g and is charged with 100g of water. The pressure inside the rocket is 100kPa gage. The exit area is one-tenth of the chamber cross-sectional area. The inside diameter of the rocket is 5cm. Assume that Bernoulli’s equation is valid for the water flow inside the rocket. Neglecting air friction calculate the maximum velocity it will attain.arrow_forwardQuestion 2: A fluid with density 1 kg/m' is moving through a pipe with same cross-sectional area at a velocity of 1.2 m/s at pointl and 1.5 m/s at point 2, and point 2 above point 1 in the elevation with 3 cm. If the pressure at the beginning at point lis 116 Pa, what is the pressure of fluid at point 2? What is the mass and volume flow rate at point 2? 2 1arrow_forwardA 400cm long pipe with a smaller diameter of 3.937 inchesand a larger diameter of 11.81 inches as shown below, isinclined at a 30° angle with the horizontal. Calculate the pressure differencein KN/m²between the smaller and bigger diameter parts of the pipe if the velocity of water at the smaller diameter section is 6.56 ft/s. Pi. V₁.d₁. A1 41-0 P2. Vz, dz. Az 32 Datumarrow_forward
- The reduced elbow shown in the figure is part of a distribution system for a fluid whose density is 0.85 and which is in a vertical plane. If the manometer at point 1 indicates 245 kPa, and the flow rate at point 1 is 0.060 m/s. a) Calculate the reactions at "x" and "y" at A to keep the elbow in placearrow_forwardProblem 4- A 400cm long pipe with a smaller diameter of 3.937 inchesand a larger diameter of 11.81 inches as shown below, isinclined at a 30° angle with the horizontal. Calculate the pressure differencein KN/m²between the smaller and bigger diameter parts of the pipe if the velocity of water at the smaller diameter section is 6.56 ft/s. P1, V₁, d₁, A₁ ²1-0 P2, V₂, d₂, A₂ ST 22 Datumarrow_forwardAir flows at the rate of 1.5m/s through a horizontal pipe with a gradually reducing cross-section as shown in the figure. The two cross-sections of the pipe have diameters of 400mm and 200 mm. Take the air density as 1.2 kg/m³ and assume inviscid incompressible flow. The change in pressure (P2-Pj) (in kPa) between sections 1 and 2 is 200mm ! (1) ↑ Air Flow 400mm (2) 1.5 m³ /s (A) –1.28 (B) 2.56 (C) -2.13 (D) 1.28arrow_forward
- Air flows steadily between two sections in a long straight portion of 0.2 m inside diameter pipe as shown below. If the density of air at entrance and exist sections are p1 =1.21 kg/m3, p2 =1.47 kg/m3, calculate the average exist velocity V2 if the velocity at entrance is V1=152 m/s. D Section (1) Section (2) P1 = 100 Kpa (abs) P2 = 300 Kpa (abs)arrow_forwardThe Water is flowing through a pipe having diameter 350 mm and 210 mm at the bottom and upper end respectively. The intensity of pressure at the bottom end is 25.85 N/cm? and pressure at the upper end is 11.6325 N/cm? & the rate of flow through the pipe is 40 lit/s. Draw a neat diagram and determine the following: 1.Velocity head at bottom of the pipe in m/s. 2. Velocity head at top of the pipe in m/s. 3. The difference in datum head between top & bottom in meter of water - 4. The difference of pressure head between bottom to top end in meter of water.- The velocity of flow of water at the bottom in m/s.arrow_forwardA 400cm long pipe with a smaller diameter of 3.937 inchesand a larger diameter of 11.81 inches as shown below, isinclined at a 30° angle with the horizontal. Calculate the pressure differencein KN/m²between the smaller and bigger diameter parts of the pipe if the velocity of water at the smaller diameter section is 6.56 ft/s. P1, V₁, d₁, A₁ ²1-0 P2, V₂, d₂, A₂ ↑ Z2 Datumarrow_forward
- The velocity profile of a liquid flows through the z direction of the vertical tube (figure right) with the radius n is given as; 1 dp (r2 – r3) 2µ dz Vz Specify the max imum velocity and derive an expression for the average velocity.arrow_forwardH.W (03-03-2021): The rectangular duct section of 400mm*300mm size carries 50 m^3/min of air, with density 1.2 kg/m^3. Where the f=0.015 A- Determine the equivalent diameter of circular duct if: 1. when the quantity of air passing through the rectangular and circular ducts is same. 2. when the velocity of air passing through the rectangular and circular ducts is same. B- Determine the pressure loss per 75m length of rectangular duct. C- Determine the pressure loss per 75m length of equivalent diameter of circular duct, when the quantity and velocity of air passing through the restenulos anguler ond eiroulor ducts is same .arrow_forwardWater with density Pwater = 1000 kg/m³ flows through a pipe, composed of two reduced in size sections, as shown on the figure. The two sections are Ilinked with a flange connection, and the corresponding diameters are D, = 8 cm and D, = 5 cm. If the velocity in cross-section 1 is v, = 5 m/s, and the readings of the connected liquid manometer is h = 60 cm, determine the reaction force acting over the flange connection. The manometric fluid is mercury, with density Pa-101kPa %3D Mercury Pmercury = 13600 kg/m³.arrow_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