Fox and McDonald's Introduction to Fluid Mechanics
9th Edition
ISBN: 9781118912652
Author: Philip J. Pritchard, John W. Mitchell
Publisher: WILEY
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Chapter 7, Problem 8P
Experiments show that the pressure drop for flow through an orifice plate of diameter d mounted in a length of pipe of diameter D may be expressed as
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Viscosity can be measured by flow through a thin-bore or
capillary tube if the flow rate is low. For length L, (small)
diameter D« L, pressure drop Ap, and (low) volume flow
rate Q, the formula for viscosity is u = D'Ap/(CLQ), where
C is a constant.
(a) Verify that C is dimensionless. The following data are
for water flowing through a 2-mm-diameter tube which
is 1 meter long. The pressure drop is held constant at
Ap = 5 kPa.
T, °C
10.0
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70.0
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0.091
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In a wind tunnel lab, the pitot tube is located at the height of 2
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Pa, if we assume the flow in the test section follow the profile
of exponential function with a-0.22. Please calculated the wind
velocity at the height of 1m. p=1.22kg/m³.
(continued 1) Measured pressures at points A, B and C as
follows: P-25 Pa, P=-55 Pa, P=-43 Pa, please calculate the
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A
C
When fluid in a pipe is accelerated linearly from rest, it begins as laminar flow andthen undergoes transition to turbulence at a time ttr which depends upon the pipe diameter D,fluid acceleration a, density ρ, and viscosity µ. Arrange this into a dimensionless relationbetween ttr and D.
Chapter 7 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Ch. 7 - The slope of the free surface of a steady wave in...Ch. 7 - One-dimensional unsteady flow in a thin liquid...Ch. 7 - In atmospheric studies the motion of the earths...Ch. 7 - Fluid fills the space between two parallel plates....Ch. 7 - By using order of magnitude analysis, the...Ch. 7 - Consider a disk of radius R rotating in an...Ch. 7 - An unsteady, two-dimensional, compressible,...Ch. 7 - Experiments show that the pressure drop for flow...Ch. 7 - At very low speeds, the drag on an object is...Ch. 7 - We saw in Chapter 3 that the buoyant force, FB, on...
Ch. 7 - Assume that the velocity acquired by a body...Ch. 7 - Derive by dimensional analysis an expression for...Ch. 7 - The speed of shallow water waves in the ocean...Ch. 7 - The speed, V, of a free-surface wave in shallow...Ch. 7 - The boundary-layer thickness, , on a smooth flat...Ch. 7 - The speed, V, of a free-surface gravity wave in...Ch. 7 - Derive an expression for the velocity of very...Ch. 7 - Derive an expression for the axial thrust exerted...Ch. 7 - Derive an expression for drag force on a smooth...Ch. 7 - The energy released during an explosion, E, is a...Ch. 7 - Measurements of the liquid height upstream from an...Ch. 7 - The load-carrying capacity, W, of a journal...Ch. 7 - Derive an expression for the drag force on a...Ch. 7 - A circular disk of diameter d and of negligible...Ch. 7 - Two cylinders are concentric, the outer one fixed...Ch. 7 - The time, t, for oil to drain out of a viscosity...Ch. 7 - You are asked to find a set of dimensionless...Ch. 7 - A continuous belt moving vertically through a bath...Ch. 7 - Derive an expression for the frictional torque...Ch. 7 - Tests on the established flow of six different...Ch. 7 - The power, P, required to drive a fan is believed...Ch. 7 - The sketch shows an air jet discharging...Ch. 7 - The diameter, d, of bubbles produced by a...Ch. 7 - Choked-flow nozzles are often used to meter the...Ch. 7 - A large tank of liquid under pressure is drained...Ch. 7 - Spin plays an important role in the flight...Ch. 7 - The power loss, P, in a journal bearing depends on...Ch. 7 - The thrust of a marine propeller is to be measured...Ch. 7 - The rate dT/dt at which the temperature T at the...Ch. 7 - When a valve is closed suddenly in a pipe with...Ch. 7 - An airship is to operate at 20 m/s in air at...Ch. 7 - An airplane wing of 3 m chord length moves through...Ch. 7 - A flat plate 1.5 m long and 0.3 m wide is towed at...Ch. 7 - This 1:12 pump model using water at 15C simulates...Ch. 7 - An ocean-going vessel is to be powered by a...Ch. 7 - On a cruise ship, passengers complain about the...Ch. 7 - A 1:3 scale model of a torpedo is tested in a wind...Ch. 7 - A flow rate of 0:18 m3/s of water at 20C...Ch. 7 - A force of 9 N is required to tow a 1:50 ship...Ch. 7 - An airplane wing, with chord length of 1.5 m and...Ch. 7 - A water pump with impeller diameter of 24 in. is...Ch. 7 - A model hydrofoil is to be tested at 1:20 scale....Ch. 7 - A ship 120 m long moves through freshwater at 15C...Ch. 7 - A 1:30 scale model of a cavitating overflow...Ch. 7 - In some speed ranges, vortices are shed from the...Ch. 7 - A 1:8 scale model of a tractor-trailer rig is...Ch. 7 - On a cruise ship, passengers complain about the...Ch. 7 - When a sphere of 0.25 mm diameter and specific...Ch. 7 - The flow about a 150 mm artillery projectile which...Ch. 7 - Your favorite professor likes mountain climbing,...Ch. 7 - A 1:50-scale model of a submarine is to be tested...Ch. 7 - Consider water flow around a circular cylinder, of...Ch. 7 - A 1:10 scale model of a tractor-trailer rig is...Ch. 7 - The power, P, required to drive a fan is assumed...Ch. 7 - Over a certain range of air speeds, V, the lift,...Ch. 7 - The pressure rise, p, of a liquid flowing steadily...Ch. 7 - An axial-flow pump is required to deliver 0.75...Ch. 7 - A model propeller 1 m in diameter is tested in a...Ch. 7 - Consider Problem 7.38. Experience shows that for...Ch. 7 - Closed-circuit wind tunnels can produce higher...Ch. 7 - A 1:16 model of a bus is tested in a wind tunnel...Ch. 7 - The propagation speed of small-amplitude surface...
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- When fluid in a pipe is accelerated linearly from rest, it begins as laminar flow andthen undergoes transition to turbulence at a time ttr which depends upon the pipe diameter D,fluid acceleration a, density ρ, and viscosity µ. Arrange this into a dimensionless relationbetween ttr and D. (Fluid Mechanics)arrow_forwardThe thrust force, F generated by a propeller is found to depend on the followingparameters: diameter D, forward velocity u, density ρ, viscosity µ and rotationalspeed N. Determine the dimensionless parameters to correlate the phenomenonarrow_forwardWhen fluid in a pipe is accelerated linearly from rest, itbegins as laminar flow and then undergoes transition toturbulence at a time t tr that depends on the pipe diameterD , fluid acceleration a , density ρ , and viscosity μ .Arrange this into a dimensionless relation between t trand D .arrow_forward
- The pressure drop (Ap) test is carried out using a pipe configuration as illustrated below: Manometer 1 Manometer 2 straight pipe D= 2R R= radius in pipe The pipe data and the flowing fluid are as follows: Pipe: D = 1 cm; L= 100 cm. Fluid: Water, with density (A) = 1000 kg/m"; absolute viscosity (u) = 0.001 kg/im.s); Experimental data is shown as shown in the following table: Task: Ja. Plot the graph of the pressure as a function of the average velocity (V.v). b. Based on the equation for laminar flow in the pipe as follows: Ap = 32VuL, Vavg (m/s) Ap (Pa) 0,001 0,002 0,005 0,01 0,02 0,04 0,06 0,08 0,1 0,12 0,15 0,30 0,62 1,61 3,10 6,10 12,10 20,10 26,00 32,50 38,90 47,20 D Compare the experimental results in the table with the results of calculations using the above equation. Leave a comment. Note: Ap = p1-p2. c. The coefficient of friction (f) in the pipe is formulated as follows: f- 2DAD PL(V.) plot (plot) this distribution of fas a function of the Reynolds number (Re). Re is…arrow_forwardIn the orifice and Jet flow experiment, the following data were collected: Water level = 30 cm , Volume V {V} L was collected in time 32 seconds, orifice diameter = 6 mm, X1 = 50 mm , X2 = 100 mm, X3 = 150 mm, X4 = 200 mm, X5 = 250 mm Y1 = 3 mm, Y2 = 10 mm, Y3 = 22 mm, Y4 = 38 mm, Y5 = 63 mm What is the actual velocity of water jet that leaves the orifice (m/s)?arrow_forwardIn falling ball viscometer experiment, the viscometer with a calibration factor K=0.3 is used to measure the viscosity of oil with density p3D 0.8 gr/cm and the density of Tantalum ball is 16.6 gr/cm, if the ball is observed to fall 250 mm in time 50.3 sec. What is the viscosity of the oil (in cp)?arrow_forward
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