1. Dimensional Analysis of Fluid Flow in a PipeConsider fluid flow in a long cylindrical pipe of diameter D. A fluid with viscosity i anddensity p flows through the pipe with an average velocity of V. The internal surface of thepipe is rough, with the average height of the roughness being h. We wish to determine howthe pressure gradient dp/dz depends on the properties of the system through dimensionlessgroups.(a) Identify the relevant parameters and their dimensions.(b) Determine the number of relevant non-dimensional groups.(c) Select the dimensionally-independent scaling variables.(d) Determine the dimensionless group that relates dp/dz to the other relevant dimen-sionless groups.

The first three parts of this problem have been solved. (a) Given: The diameter of the long…

Answered: 1. Dimensional Analysis of Fluid Flow…

Similar questions

A viscous fluid flows in two different pipes. Pipe 1 has a radius r1, and Pipe 2 has a radius r2. If both pipes have the same length and r1 > r2, choose the correct statement about the pressure difference of the fluid in Pipe 1 and Pipe 2 The pressure difference of the fluid is the same in Pipe 1 and Pipe 2. The fluid in Pipe 1 has larger pressure difference. It cannot be determined in which pipe the fluid has larger pressure difference. The fluid in Pipe 2 has larger pressure difference.
Three glass containers containing water of the same temperature have different shapes and thickness. The distance between the top surface of the water and the bottom of each glass container is the same. Which of the following statements correctly characterizes the pressure at the bottom of the glass containers? (explain why) 2 3 a. Pressure at the bottom of all glass containers is the same. b. Pressure at the bottom of (2) and (3) are the highest because they have the same volume. c. Pressure at the bottom of (2) is the highest because it is wide. d. Pressure at the bottom of (1) is the highest because it is narrow. e. Pressure at the bottom of (3) is the highest because it is vertically aligned.
Air P = 76 kPa SG₁ = 13.55 40 cm 22 cm Consider a dual-fluid manometer attached to an air pipe as shown in the image. If the SG of one fluids is 13.55, determine the SG of the other fluid for the indicated absolute pressure of air. Take the atmospheric pressure to be about 100 kPa. SG₂
Ethanol is flowing in a pipe and at all points completely fills the pipe. At point A in the pipe the gauge pressure is p and the cross-sectional area of the pipe is 0.0500 m² . The other end of the pipe (point B) is open to the air, has cross-sectional area 0.0120 m2, and is at a vertical height of 9.00 m above point A. Part A What must the gauge pressure p be at A if the volume flow rate out of the pipe at point B is 0.0800 m /s? Express your answer with the appropriate units. HA ? x" X•10" p = 1.87 • 10$ Pa This unit is not recognized. See the list of acceptable units. No credit lost. Try again. Submit Previous Answers Request Answer Provide Feedback MacBook Air