1. To find dimensionless groups that describe flow through a cylindrical tube using Dimensional Analysis. The pressure drop AP (ML" T-2) across a cylindrical tube depends on the following variables: Fluid density p (ML³) Fluid viscosity u (ML¹ T¹) Tube diameter D (L) Tube roughness k (L) Tube length L (L) Fluid average velocity (LT) To find a dimensionless group involving AP depends on a dimensionless group involving and perhaps other dimensionless groups. a) How many dimensionless groups can be formed from this set of variables? b) Select an appropriate set of core variables for this problem c) Find the dimensionless group involving AP. 2. Spin plays an important role in the flight trajectory of golf, Ping-Pong, and tennis balls. Therefore, it is important to know the rate at which spin decreases for a ball in flight. The aerodynamic torque, T, acting on a ball in flight, is thought to depend on flight speed, V, air density, p, air viscosity, μ, ball diameter, D, spin rate (angular speed), 0, and diameter of the dimples on the ball, d. Determine the dimensionless parameters that result. 3. The fluid velocity (v) of a flow-measuring nozzle is presumed to be a function of the pipe diameter (d), fluid density (p), nozzle diameter (a), fluid viscosity (u), and pressure drop (Ap). Find an appropriate set of dimensionless parameters that describe this system using the Buckingham Pi method.
1. To find dimensionless groups that describe flow through a cylindrical tube using Dimensional Analysis. The pressure drop AP (ML" T-2) across a cylindrical tube depends on the following variables: Fluid density p (ML³) Fluid viscosity u (ML¹ T¹) Tube diameter D (L) Tube roughness k (L) Tube length L (L) Fluid average velocity (LT) To find a dimensionless group involving AP depends on a dimensionless group involving and perhaps other dimensionless groups. a) How many dimensionless groups can be formed from this set of variables? b) Select an appropriate set of core variables for this problem c) Find the dimensionless group involving AP. 2. Spin plays an important role in the flight trajectory of golf, Ping-Pong, and tennis balls. Therefore, it is important to know the rate at which spin decreases for a ball in flight. The aerodynamic torque, T, acting on a ball in flight, is thought to depend on flight speed, V, air density, p, air viscosity, μ, ball diameter, D, spin rate (angular speed), 0, and diameter of the dimples on the ball, d. Determine the dimensionless parameters that result. 3. The fluid velocity (v) of a flow-measuring nozzle is presumed to be a function of the pipe diameter (d), fluid density (p), nozzle diameter (a), fluid viscosity (u), and pressure drop (Ap). Find an appropriate set of dimensionless parameters that describe this system using the Buckingham Pi method.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. To find dimensionless groups that describe flow through a cylindrical tube using Dimensional
Analysis. The pressure drop AP (ML" T-2) across a cylindrical tube depends on the following
variables:
Fluid density p (ML³)
Fluid viscosity u (ML¹ T¹)
Tube diameter D (L)
Tube roughness k (L)
Tube length L (L)
Fluid average velocity <v> (LT)
To find a dimensionless group involving AP depends on a dimensionless group involving <v> and
perhaps other dimensionless groups.
a) How many dimensionless groups can be formed from this set of variables?
b) Select an appropriate set of core variables for this problem
c) Find the dimensionless group involving AP.
2. Spin plays an important role in the flight trajectory of golf, Ping-Pong, and tennis balls. Therefore, it is
important to know the rate at which spin decreases for a ball in flight. The aerodynamic torque, T,
acting on a ball in flight, is thought to depend on flight speed, V, air density, p, air viscosity, μ, ball
diameter, D, spin rate (angular speed), 0, and diameter of the dimples on the ball, d. Determine the
dimensionless parameters that result.
3. The fluid velocity (v) of a flow-measuring nozzle is presumed to be a function of the pipe diameter (d),
fluid density (p), nozzle diameter (a), fluid viscosity (u), and pressure drop (Ap). Find an appropriate
set of dimensionless parameters that describe this system using the Buckingham Pi method.
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