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Concept explainers
Fully developed flow moving through a 40-cm diameter pipe has the following velocity profile:
Radius, r, cm | 0.0 | 2.5 | 5.0 | 7.5 | 10.0 | 12.5 | 15.0 | 17.5 | 20.0 |
Velocity, v, m/s | 0.914 | 0.890 | 0.847 | 0.795 | 0.719 | 0.543 | 0.427 | 0.204 | 0 |
Find the volume flow rate Q using the relationship
wherer is the radial axis of the pipe, R is the radius of the pipe, and v is the velocity. Solve the problem using two different approaches.
(a) Fit a polynomial curve to the velocity data and integrate analytically.
(b) Use multiple-application Simpson's
(c) Find the percent error using the
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Chapter 24 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- Find the pressure drop between locations a and b for flow in a pipe using the following data: Working fluid: Water Pipe: Stainless steel, Schedule No. 120 Nominal pipe size (cm): 10 Flow rate (m3 /min): 2.271 Temperature (C): 38 Length (m): 45.72 Solve for the following 3 cases: a) Za = Zb =33.5 m, b) Za = Zb + 15 m, and c) Za = Zb + 46 m.arrow_forward7. An oil (sp.gr 0.9) is flowing through a 1.2m diameter pipe at a rate of 2.5 m³/s. The kinematic viscosity of oil is 3 X106 m²/s. In order to model this flow, water is used to flow through a 120mm diameter pipe having kinematic viscosity of 0.012X104 m²/s. Find the model discharge and velocity.arrow_forwardQUESTION 1 Three pipes A, B, and C are interconnected as shown in figure 1. The pipe dimensions are as follows: Pipeline A в D (cm) 15 10 L (m) 300 f 0.01 240 0.01 20 600 0.005 A 15 m 25 m В Figure 1 1.1 Find the rate at which water will flow in each pipe, ignoring the shock losses at P and entry to pipelines A and B. 1.2 Find the pressure at P.arrow_forward
- Fluid originally flows through a tube at a rate of 110 cm3 /s. To illustrate the sensitivity of flow rate to various factors, calculate the new flow rate for the following changes with all other factors remaining the same as in the original conditions.Randomized VariablesPx = 2.5ηx = 3.2rx = 0.14lx = 4.6Q = 110 cm3/s Part (a) Calculate the new flow rate in cm3/s if the pressure difference increases by a factor of 2.5 . Part (d) Calculate the new flow rate if another tube is used with a radius 0.14 times the original. Part (e) Calculate the new flow rate if yet another tube is substituted with a radius 0.14 times the original and half the length, and the pressure difference is increased by a factor of 2.5.arrow_forwardPROBLEM #1: Complete the data of the table below. Copy the entire table in your paper and use a different colored pen for your answers, you may also box your answers. Show solution. T:K P: kPa H: kJ/kg U: kJ/kg State (if wet steam provides xv as well) 1 525 350 2 125 2700 3 455.15 750 4 600 Xv = 0.8 5 200 1800 PROBLEM #2 A nozzle is used to increase the velocity of steam before it enters a turbine as a part of a power plant. The steam entering is at 1 MPa, 500 K and leaves at the conditions of 350°C and 2 MPa. If the nozzle has an inlet diameter of 3 cm and an outlet diameter of 1 cm, how much is transferred during the process? Is it lost or gained?arrow_forward(b) A pitot-static probe is use to determine the flow velocity by measuring the differential pressure. The pitot formula to obtain the flow velocity is, 2(P- P,) V = where, V is the velocity, P is pressure and pis fluid density. i) The pressure difference sensor use in the system is electronic types and the output of the device is measured in voltage. The output of the pressure device is 3.5 V and the linear relationship between the device and the pressure difference is 10 kPa/V. If the measured fluid is water at 20°C, determine the pressure difference inside the system the water velocity. ii) The Pitot-static tube is also commonly use in aircraft. An aircraft flying at 3000 m above sea level when the differential pressure reading clocked 3 kPa. Determine the speed of the aircraft.arrow_forward
- G1/ in the Pipe (A) is equal (PA= 25 Lit15), the diameter is equal ( DA - 75mm, Do = Fig.shown, the Flow rate in 6o mm, Dg = Dc%=30 mm), and the velocit Pipe (D) is equal (U0=5m/s), the relation between flow rate in Pipe (B) and pipe (c) %3D Find the Value af . 2- Un, UB, Uc. water Os = 30 mm input A QA - 25 Lit/sec = 75 mm fo mm %3D Inpud = A outPut = B,C,D accumule tion =o.arrow_forward1. The observed and model simulated average daily flow in month flow at the outlet of a river catchment during a given period is presented as follows. Predicted flow Observed flow 0.25 0.30 0.70 0.73 0.80 0.87 0.71 0.90 0.71 0.65 1.60 1.45 0.90 0.70 0.71 0.61 0.24 0.22 1.00 0.64 0.81 1.00 1.05 0.90 0.46 0.48 0.27 0.23 0.80 0.24 0.32 0.42 0.80 0.89 (i) Evaluate the model performance based on any two computed statistical measures of performance of your choice. (ii) Explain possible reasons for model performance observed in (i) above. (Hint: Refer to reading material provided on model evaluation by Moriasi et al., 2007)arrow_forward1. Start from the following equations from class notes (treat as given): The shear stress in pipe flow T = -μ- dr du 16 [1-(-)²), AP D² 16μL The fluid velocity in the pipe u = Derive clearly the following results: (a) The shear stress on the wall of the pipe, Tw. (b) The average velocity in the pipe flow, ū. (c) The Darcy friction factor, defined by f where L is the length of the pipe. 8 tw pū² (d) Express the result of (c) in terms of the Reynolds number, Re. (e) Find an expression for the head loss due to shear stress at the wall, AH₁, in terms of f,u, D and L. (f) What are the main assumptions in the fluid flow, in order to analyse the flow in this way?arrow_forward
- 8:55 9 27 O ll all 66% bläi 3 an the flow inside a nozzle be ?steady and uniform yes never it can be steady but never uniform it can be uniform but never steady 0 الخيار رقم 1 5 نقاط What is the pressure in Pascals at a depth of 1m below the * ?water surface 98100 pa 980 pa 98 pa 1 pa IIarrow_forwardfluid mechanics A pipe 200 (mm) diameter carries Oil at a flow rate of 0.030 (m³/s). The pipe diameter reduces from 200 (mm) to 150 (mm). Point 1 is located at the beginning of the pipe and point 2 is located at the end of the pipe. Elevation of point 1 is 165 (m) lower than elevation of point 2. Water pressure at point 2 is atmospheric pressure. Water flow in the pipe ascending from point 1 to point 2. Total head losses of flow in the pipe equals to 15 (m). 1- Find the value of pressure head of Oil at point 1. 2- Draw the H.G.L. of flow in the pipe.arrow_forwardPLBASE BOX YOUR ANSWERS 3.7 atm -: The 6 cm diameter pipe contains a liquid (p = 1260 kg/m', u = 149 kg/m.s) flowing at an unknown flowrate. Pipe length (A to B) is 40 m. For the gage-pressure measurement shown, find a) the direction of flow (1.e, AB or B→A); b) Is the flow laminar/ turbulent; and c) friction factor. Ignore minor losses. 2.1 atm 12 marrow_forward
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