Q2:- If the velocity of flow v, dynamic viscosity u, bulk modulus of elasticity K and diameter of pipe D, using dimensional analysis, determine the general form of relationship between these variables.
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- Q2:- If the velocity of flow v, dynamic viscosity a, bulk modulus of elasticity K and diameter of pipe D, using dimensional analysis, determine the general form of relationship between these variables.Q2:- If the velocity of flow v, dynamic viscosity u, bulk modulus of elasticity K and diameter of pipe D, using dimensional analysis, determine the general form of relationship between these variables.Problems H.pdf > Problems H.W: Lecture No.6 Part 2 Q1-(2.4-4, Holland): A fluid of density (p) and dynamic viscosity (u) flows in s.s in a cylindrical pipe of inside diameter (d) with mean linear velocity (u). Derive an expression for the pressure gradient AP/L in terms of p, u, d & u. By dimensional analysis (Note Lect. No.3). Q2-An oil with a viscosity of u= 0.40 N-s/m and density p= 900 kg/m flows in a pipe of diameter d= 0.20m. (a) What pressure drop, pl-p2, is needed to produce a flowrate of Q=2.0x10-5 m/s if the pipe is horizontal with xl=0 and x2=10 m? (b) How steep a hill, part (a), but with pl=p2? (c) For the conditions of part (b), if pl=200 kPa, what is the pressure at section, x3=5 m, where x is measured along the pipe? „must the pipe be on if the oil is to flow through the pipe at the same rate as in II
- (b) The kinematic viscosity of a fluid used for model is one third of the kinematic viscosity of the fluid used for prototype. During testing of the model, if viscosity and gravity forces are predominant, find the scale ration, velocity ratio and discharge rationQl:- Using the dimensional analysis, find the relationship between the variables, shear stress t, flow velocity v, density p, viscosity u and pipe diameter D.Q2) Fill in the blanks with appropriate word(s), for EXKEl of the following; K Specific weight is defined as According to the variation of density with pressure, Nuids may be classified into - Nuids and - Nuids. 3. The approximate number of experiments to evaluate the influence of 3 parameters separately is assuming that 5 experiments are needed for each variable. ¿When viscous resistance is important, -. criteria for similarity is used. S. The center of pressure is defined as - A Hydrostatic forces in a static fluid is the result of the exerted on submerged surfaces. Streamline is defined as Continuity equation represents the d 0, conservation of
- The resistance R, to the motion of a completely submerged body depends upon the length of the body L, velocity of flow V, mass density of fluid p and kinematic viscosity of fluid v. By dimensional analysis prove that R = pr* L') VL' = pV?1Question 2: The pressure drop, AP, in a horizontal pipe depends on the pipe diameter, d, pipe length, L, pipe roughness, &, average velocity, V, density of the fluid, p, and absolute viscosity of the fluid, u. Express the variables in non-dimensional form using Buckhingham-Pi theorem (25 Points)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.
- Using II-Theorem method to Express (n) in terms of dimensionless groups.The efficiency (n) of a fan depends upon density (p), and dynamic viscosity (u), of the fluid, angular velocity (@), diameter of the rotator (D), and discharge (Q). Q3/ A petroleum crude oil having a kinematics viscosity 0.0001 m?/s is flowing through the piping arrangement shown in the below Figure,The total mass flow rate is equal 10 kg/s entering in pipe (A) . The flow divides to three pipes ( B, C, D). The steel pipes are schedule 40 pipe. note that the dynamic viscosity 0.088 kg/m.s. Calculate the following using SI units: 1- The type of flow in pipe (A). 2- The mass velocity in pipe (B) GB. 3- The velocity in pipe (D) Up. 4- The Volumetric flow rate in pipe (D) QD. 5- The Volumetric flow rate in pipe (C) Qc. Og = 2o mm Ug = 2UA Perolenm crude oIL A ma = 1o Kg/s O = 5o mm mic = ? Go = 7000 k9/m.s Nate that!- O, = 30 mm. D:0iameter. U:velocity G mass velocity mimass How vateThe laminar flow of a fluid with a constant viscosity, 4, inside a channel is governed by the following boundary value problem (strong form): d'u dp for y E (0, h) "dy dr u = 0 at y = 0 and y = h vhere u is the fluid velocity and is the pressure drop in the direction of the flow. a) Derive the weak form of the boundary value problem described above.Q2 :-If the velocity of flow over surface v, Surface tension ô, density of flow p length of surface L, and pressure p, using dimensional analysis, determine the general form of relationship between these variables.