c) The drag force Fp on a cylinder of diameter d and length / is to be studied. What functional form relates the dimensionless variables if a fluid with velocity V flows normal to the cylinder?
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- Q1: Consider laminar flow over a flat plate. The boundary layer thickness o grows with distance x down the plate and is also a function of free-stream velocity U, fluid viscosity u, and fluid density p. Find the dimensionless parameters for this problem, being sure to rearrange if neessary to agree with the standard dimensionless groups in fluid mechanics. Answer: Q2: The power input P to a centrifugal pump is assumed to be a function of the volume flow Q, impeller diameter D, rotational rate 2, and the density p and viscosity u of the fluid. Rewrite these variables as a dimensionless relationship. Hint: Take 2, p, and D as repeating variables. P e paD? = f( Answer:A boundary layer is a thin region (usually along a wall) in which viscous forces are significant and within which the flow is rotational. Consider a boundary layer growing along a thin flat plate. The flow is steady. The boundary layer thickness ? at any downstream distance x is a function of x, free-stream velocity V∞, and fluid properties ? (density) and ? (viscosity). Use the method of repeating variables to generate a dimensionless relationship for ? as a function of the other parameters. Show all your work.The drag force FD on a cylinder of diameter d and length l is to be studied. What functional form relates the dimensionless variables if a fluid with velocity V flows normal to the cylinder?
- MLT By dimensional analysis, obtain an expression for the drag force (F) on a partially submerged body moving with a relative velocity (u) in a fluid; the other variables being the linear dimension (L), surface roughness (e), fluid density (p), and gravitational acceleration (g).The wall shear stress Twin a boundary layer is assumed to be a function of stream velocity U, boundary layer thickness , local turbulence velocity u', density p, and local pressure gradient dp/dx. Using (p, U, and ) as repeating variables, rewrite this relationship as a dimensionless function.Force F is applied at the tip of a cantilever beam of length L and moment of inertia I Fig. . The modulus of elasticity of the beam material is E. When the force is applied, the tip deflection of the beam is z d.Use dimensional analysis to generate a relationship for zd as a function of the independent variables. Name any established dimensionless parameters that appear in your analysis
- Consider laminar flow over a flat plate. The boundary layer thickness & grows with distance x down the plate and is also a function of free-stream velocity U, fluid viscosity u, and fluid density p. Find the dimensionless parameters for this problem, being sure to rearrange if necessary to agree with the standard dimensionless groups in fluid mechanics.Q1) Under laminar conditions, the volume flow rate Q through a small triangular-section pore of side length (b) and length (L) is a function of viscosity (u), pressure drop per unit length (AP/L), and (b). Using dimensional analysis to rewrite this relation. How does the volume flow changes if the pore size (b) is doubled?During World War II, Sir Geoffrey Taylor, a British fluid dynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumed that the energy released E, was a function of blastwave radius R, air density ρ, and time t. Arrange these variables into single dimensionless group, which we mayterm the blast wave number.
- Problem 1: The discharge pressure (P) of a centrifugal pump shown below is a function of flow rate (Q), impeller diameter (D), fluid density (p), and impeller angular speed (12). P = f (Q. D, p. 92). Use the Buckingham pi technique to rewrite this function in terms of dimensionless parameters, 1 g (n₂). P= P(Q,D, Dimensions 2) N= 5 Q. PUsing 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 vateConsider fully developed flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary. The flow is steady, incompressible, and two-dimensional in the xy-plane. a) Use the first principle (dimensional analysis) to generate a dimensionless relationship for the x-component of fluid velocity u as a function of fluid viscosity μ, top plate speed v, distance h, fluid density ρ, and distance y. b) Name the common dimensionless number formed in (a). Hint: modifying the dimensionless number if necessary.