Solution:
Total number of variables given,
Total number of variables,
Number of fundamental variables,
Therefore, number of
terms will be,
Therefore needed number of pi groups is 3
A given problem to be solved using dimensional analysis consists of the following assumed functional relationship:...
b) The power input P to be a cerki fugal pump is assumed to be a function of the volume flow , impeller diometer D rotational rate , and the density and MJ CAST of the fluid. By using , and D as repeating von bles) develop this as a dimensionless relationship - d3 - A water solution entering the propeller in the pump produces thrust force, ft which is depending on the density, diameter ,d, the rotational speed, co...
Which of the following are acceptable Pi terms for the
dimensional relationship
where ?p is a pressure difference, D is a diameter, V is a
velocity, and ? and ? are the fluid density and viscosity? Can
select multiple answers.
a)
b)
c)
d)
I will give rating for the complete answer ?
(a) Using dimensional analysis, express the characteristic length, velocity and time scales for near-wall flow in terms of the density, viscosity and wall shear-stress. Show that the length scale can also be expressed as where v is the kinematic viscosity and uy is the friction velocity (10 marks) Ut
Using dimensional analysis, express the characteristic length, velocity and time scales for near-wall flow in terms of the density, viscosity and wall shear-stress. Show that the length scale can also be expressed as where v is the kinematic ur viscosity and u, is the friction velocity.
3- Through a dimensional analysis, express the following equation for a bubble in a dimensionless form, and show which dimensionless parameters will be finally produced. (Use the characteristic velocity U, and length L for nondimensionalizing procedure.) Pb(t) - po(t) dR 3 R 2 4V dR 2S + P2+- d+2 PL Rdt PLR PL is the density of the surrounding liquid of the bubble R is the radius of the bubble t is the time U is the kinematic viscosity of...
A bridge is supported by two types of rectangular cross-section piles located in a river as shown in Figure 1. The width of the piles is w 0.5 m and their lengths are either l-2 m or 12 = 2.5 m. The river of depth of about 20 m runs at 2 m/s. Water density is ρ = 1000 kg/mand its absolute viscosity 1.00 x 10-3 N.s/m2 You are asked to perform dimensional analysis to find the drag force on...
A bridge is supported by two types of rectangular cross-section piles shown in Figure I. The width of the piles is w 0.5 m and their lengths are either li-2 m or l2 2.5 m. The river of depth of about 20 m runs at 2 m/s. Water density is p 1000 kg/m and its absolute viscosity 1.00 x 10-3 N.s/m2. located in a river as You are asked to perform dimensional analysis to find the drag force on the...
A bridge is supported by two types of rectangular cross-section piles located in a river as shown in Figure 1. The width of the piles is w - 0.5 m and their lengths are either l 2 m or 12 2.5 m. The river of depth of about 20 m runs at 2 m/s. Water density is p 1000 kg/m and its absolute viscosity 1.00 x 10-3 N.s/m2 You are asked to perform dimensional analysis to find the drag force...
Density p [kg/m2], viscosity - u [kg/ms], surface tension - o (N/m=kg/s2] compressibility K [Pa-kg/ms2] 1. For particles settling in a stationary fluid it is thought that the drag force FD of a small sphere is a function of the settling velocity of the sphere - V, the diameter of the sphere - d, and the density p, and viscosity of the fluid - . Determine the dimensionless relationship(s) between these variables (FD/HVd, pdV/H) 2. (a) The efficiency of a...
A bridge is supported by two types of rectangular cross-section piles located in a river as shown in Figure 1. The width of the piles is w -0.5 m and their lengths are either lı- 2 m or l2-2.5 m. The river of depth of about 20 m runs at 2 m/s. Water density is p 1000 kg/m3 and its absolute viscosityH 1.00 x 10-3 N.s/m2. You are asked to perform dimensional analysis to find the drag force on the...