The Power (P) required to drive the pump depends upon the diameter (D), the angular velocity (@), the discharge (Q), and the fluid density (p). Drive expression for (P) by dimensional analysis. Ans. P= o p D° .)
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- Figure shows the flow of water over a dam. Thevolume fl ow Q is known to depend only on crest width B ,acceleration of gravity g , and upstream water height Habove the dam crest. It is further known that Q is proportionalto B . What is the form of the only possible dimensionallyhomogeneous relation for this flow rate?As a mechanical engineer, you can predict the performance of a new centrifugal pump using two methods which are One Dimensional Analysis (Velocity Triangle) and Hydraulic Scaling. Describe the limitation of each method.The time t d to drain a liquid from a hole in the bottom of atank is a function of the hole diameter d , the initial fluidvolume y 0 , the initial liquid depth h 0 , and the density ρ andviscosity μ of the fluid. Rewrite this relation as a dimensionlessfunction, using Ipsen’s method.
- List the three primary purposes of dimensional analysis.Determine the form of an equation for the distance (s) that a sphere will fall in time t, if it starts with an initial velocity and the resistance of the fluid through which it falls is taken into consideration. Resistance is dependent upon the density (ρ) and viscosity (μ) of the medium and the diameter (d) and mass (m) of the sphere. Hence in addition to g, v and t these factors are incorporated. S = f (g, v, t, m, d, ρ, μ) USE DIMENSIONAL ANALYSIS AND BUCKINGHAM PI THEOREMThe power input P to a centrifugal pump is assumed to be a function of the volume flow Q, impeller diameter D, rotational rate Ohm, the density rho, and viscosity mu of the fluid. Rewrite this as a dimensionless relationship
- An impeller (axial-flow turbine propeller) in an agitated tank has an output torque (T) whose dimension is ML2/T2 which is proportional to the volumetric flow rate (Q) and also depends upon the density (ρ), rotor diameter (D), and rotation rate (N). Perform Dimensional Analysis.Prove that the pressure at a point is equal in all directions for a fluid at rest with respect to thestationary Cartesian coordinate system XYZ. Comparatively analyse also the definitions of stress andpressureBy 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).
- For Piper PA-24 Comanche (Wing area=16.5m^2,wing span=10.97m), what is the mean aerodynamic chord (in meters) main wing. And the distance between the quarter chord location of the mean aerodynamic centre of the main wing and the horizontal wing (in metersThe Archimedes number, Ar, used in the flow of stratifiedfluids, is a dimensionless combination of gravity g , densitydifference Δ ρ , fluid width L , and viscosity μ . Find theform of this number if it is proportional to g .1) When doing the dimensional analysis, the model fluid should be the same with prototype fluid. True or False 2) What is the unit of Reynolds number (Re)? a) Dimensionless b) m/s c) m2/s d) m/s2