q; = K(P; − P;)-qjq; = K(P; - P;)where qi and q; are fluid flow at nodes i and j, respectively; P; and P; arefluid pressure at nodes i and j, respectively; and K isK=πD4128μLwhere D is the diameter of the piper, μ is the viscosity, and L is the lengthof the pipe. The fluid flow is considered positive away from the node. Theviscosity of the fluid is 9×10+ Pa's.a. Write the element matrix equation for the flow in the pipe element.b. The net flow rates into nodes 1 and 2 are 10 and 15 m³/s, respectively.The pressures at the nodes 6, 7, and 8 are all zero. The net flow rate intothe nodes 3, 4, and 5 are all zero. What is the outflow rate for elements 4,6, and 7?Q1213(4)410567Elem1234567D(mm) 40405025402525L(m)1142338

Answered: Image /qna-images/answer/a734ae54-530c-4b00-b07a-026106b326b4.jpg

Answered: q; = K(P; − P;) - qj q; = K(P; - P;)…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Q4/ An orifice meter is used to measure the rate of flow of a fluid in pipes. The flow rate is related to the pressure drop by the following equation: |ΔΡ u = c where u = fluid velocity AP = pressure drop (force per unit area) p = density of the flowing fluid C = constant What are the units of c in the SI system of units?
% ParametersD = 0.1; % Diameter of the tube (m)L = 1.0; % Length of the tube bundle (m)N = 8; % Number of tubes in the bundleU = 1.0; % Inlet velocity (m/s)rho = 1.2; % Density of the fluid (kg/m^3)mu = 0.01; % Dynamic viscosity of the fluid (Pa.s) % Define the grid size and time stepdx = D/10; % Spatial step size (m)dy = L/10; % Spatial step size (m)dt = 0.01; % Time step size (s) % Calculate the number of grid points in each directionnx = ceil(D/dx) + 1;ny = ceil(L/dy) + 1; % Create the velocity matrixU_matrix = U * ones(nx, ny); % Perform the iterationsfor iter = 1:100 % Calculate the velocity gradients dUdx = (U_matrix(:, 2:end) - U_matrix(:, 1:end-1)) / dx; dUdy = (U_matrix(2:end, :) - U_matrix(1:end-1, :)) / dy; % Calculate the pressure gradients dpdx = -mu * dUdx; dpdy = -mu * dUdy; % Calculate the change in velocity dU = dt * (dpdx / rho); % Update the velocity matrix U_matrix(:, 2:end-1) = U_matrix(:, 2:end-1) + dU; % Apply…
TRUE OR FALSE: Any equation that comes out of the differential approach is valid at every point in the flow field. On the other hand, the integral approach gives us a point by point value and not an average value. A crude oil with a density of 875 kilogram per cubic meter is pumped and flowing at 1.5 meter per second through a pipeline 1 meter in diameter. The maximum viscosity of the oil to exhibit a laminar flow behavior is 625 centipoise. Using conservation equation in fluid flow i. e. continuity equation, the set of velocity component below represent a possible incompressible flow: u = 3xy ; v = x3 - xy3
Pi constant to be used: 3.14159 Capillary tube: radius = 0.02 cm; length = 9 cm; pressure = 0.7 mmHg Liquid sample: density = 4 ml; time of flow = 4.5 seconds Determine (a) pressure in MKS unit, (b) pressure in CGS unit, (c) the viscosity of the liquid, (d) If the weight was given as 8.5 grams, what will be the density of the liquid? (e) the kinematic viscosity of the liquid? (f) and the fluidity of the liquid?
(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.
Q1: Apply appropriate solution method using math principles to prove that "the pressure at a point in a fluid has the same magnitude in all directions". Support your answer with sketch. Answer: Px Pz = Pn P are the mean pressures at the three surfaces in the x- and z-directions. Q2: Formulate the issue and identify key variables to prove that [AP = P2 - P, = pg Az = y, Az], where y, and p are the specific weight and density of the fluid, respectively. Az is the vertical distance. Support your answer with sketch. Q3: From fluid mechanics science perspective, define the center of gravity and the center of pressure. Q4: Identify the hydrostatic force acting on the top surface of a submerged rectangular plate by applying principles of engineering for the following cases: 1 tilted plate, (2 vertical plate, and 3 horizontal plate. Support your answer with sketch. Q5: By applying principles of fluid mechanics science, define the "rigid-body" and identify its features. Q6: Formulate the issue…
The Reynolds number is a dimensionless group defined for a fluid flowing in a pipe as Re = Duplu where Dis pipe diameter, u is fluid velocity, p is fluid density, and u is fluid viscosity. When the value of the Reynolds number is less than about 2100, the flow is laminarthat is, the fluid flows in smooth streamlines. For Reynolds numbers above 2100, the flow is turbulent, characterized by a great deal of agitation. Liquid methyl ethylketone (MEK) flows through a pipe with an inner diameter of 2.067 inches at an average velocity of 0.48 ft/s. At the fluid temperature of 20°C the density of liquid MEK is 0.805 g/cm? and the viscosity is 0.43 centipoise [1 cP = 1.00 x 10-³ kg/(m-s)]. Without using a calculator, determine whether the flow is laminar or turbulent. Show your calculations.
Reynolds number for pipe flow may be expressed as Re = (4 m/ Trd) / µ Where m = mass flow, kg/s d= pipe diameter, m p = viscosity, k/m s In a certain system, the flow rate is 5.448 kg/min +0.5 %, through a 0.5" (inch) diameter (±0.005"). The viscosity is 1.92x 10-5 kg/m s, ±1 %. Calculate the value of the Reynolds Number and its uncertainty. Determine the main contribution to uncertainity.
Orange JO A O X 91|4 2:26 ch1_introductio.. Shear stress (t) is the resistance per unit area of the upper plate t = R/A=T/A Water responds to shear stress by continuously yielding in angular deformation in the direction of the shear. IThe rate of angular deformation in the fluid, d(8)/dt ,is proportional to the shear Istress, as shown in Figure 1.1. do dt dx ,and v = dy dx Angular deformation (Shear strain), 0 = dt do Rate of shear strain = dt dx dv (Velocity gradient) dy dy dt dv Therefore, to dv T = constant dy dv T = - dy The proportionally constant, u, is called the absolute viscosity of the flyid Example A flat plate of 50 cm² is being pulled over a fixed flat surface at a constant velocity of 45 cm/sec (Figure 1.1). An oil film of unknown viscosity separates the plate and the fixed surface by a distance of 0.1 cm. The force (T) required to pull the plate is measured to be 31.7 N, and the viscosity E of the fluid is constant. Determine the viscosity (absolute). 22 Example A flat…
Given problem: a.) At temperatures of 100° F and 120 psi absolute, calculation of above properties for methane (CH4): what is the barometric pressure if the gauge reading is 104.5 Psig? b.) A pipe transports an incompressible fluid. The volume flow rate is 10m3/s at point 1 along the pipe. The area halves at spot 2 along the pipe. At site 2, what is the volume flow rate?
Learning Portal Academic Departments ETC - CIMS - Courses - Reports - e-Services - Moham Select one: O True O False The energy loss due to the change of flowrate of a fluid flow in direction is known as minor loss. Select one: O True O False Determine the time taken by the oil to get collected in a measuring jar of 26 x 10-3 m³. The oil has the specific that has a mean velocity of 9 m/s in a pipe of cross-sectional area 11 x 10-5 m2. Time taken (in s) arch EUROSTARD
If the continuity equation for non-compressible fluid is applicable, what will happen to the air density (p) if the cross-sectional area of a tube changes? a. p1>02 b. p is dependent on the cross sectional area of the tube c. p1

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