A piston-cylinder is producing a viscous oil flow, which has the flow rate of Q, radius R=1.5 mm, and stroke L-5 mm. The fluid density is p = 800 kg/m³ and the viscosity is μ = 0.5 Pa.s. The pressure to drive the flow is p=6.25 Pa. a. How many non-dimensional groupings can be obtained? Derive them. b. If the flow transitions at Re = V(2R)-2300. Is the generated flow laminar or turbulent given Q=20 mL/s? c. Assume the pressure gradient is uniform on the cross-section and can be calculated using. The velocity profile in the cylinder is u(r) = – [1 − (²]. Sketch the velocity profile. Calculate the shear stress at the R² Op cylinder wall and label the direction. d. Calculate the flow rate Q with the velocity profile in (c).. e. If the shear stress is uniform over the cross-section, i.e. T = C, what's the pressure gradient distribution and sketch it?
A piston-cylinder is producing a viscous oil flow, which has the flow rate of Q, radius R=1.5 mm, and stroke L-5 mm. The fluid density is p = 800 kg/m³ and the viscosity is μ = 0.5 Pa.s. The pressure to drive the flow is p=6.25 Pa. a. How many non-dimensional groupings can be obtained? Derive them. b. If the flow transitions at Re = V(2R)-2300. Is the generated flow laminar or turbulent given Q=20 mL/s? c. Assume the pressure gradient is uniform on the cross-section and can be calculated using. The velocity profile in the cylinder is u(r) = – [1 − (²]. Sketch the velocity profile. Calculate the shear stress at the R² Op cylinder wall and label the direction. d. Calculate the flow rate Q with the velocity profile in (c).. e. If the shear stress is uniform over the cross-section, i.e. T = C, what's the pressure gradient distribution and sketch it?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![1. A piston-cylinder is producing a viscous oil flow, which has the flow rate of Q, radius
R=1.5 mm, and stroke L-5 mm. The fluid density is p = 800 kg/m³ and the viscosity is
μ = 0.5 Pa-s. The pressure to drive the flow is p=6.25 Pa.
a. How many non-dimensional groupings can be obtained? Derive them.
b.
If the flow transitions at Re = PV(2R) =2300. Is the generated flow laminar or
turbulent given Q=20 mL/s?
LL
c. Assume the pressure gradient is uniform on the cross-section and can be
calculated using OP=-. The velocity profile in the cylinder is u(r) =
ax
- [1-(²]. Sketch the velocity profile. Calculate the shear stress at the
R² ap
2UÔI
cylinder wall and label the direction.
d.
Calculate the flow rate Q with the velocity profile in (c)..
e. If the shear stress is uniform over the cross-section, i.e. T = C, what's the
pressure gradient distribution and sketch it?
L
L.
R](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc11810c9-3aba-424b-965a-9d4a091edf9a%2F9c1cb119-6a26-4add-9757-b08b480978ff%2Fk1nojna_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. A piston-cylinder is producing a viscous oil flow, which has the flow rate of Q, radius
R=1.5 mm, and stroke L-5 mm. The fluid density is p = 800 kg/m³ and the viscosity is
μ = 0.5 Pa-s. The pressure to drive the flow is p=6.25 Pa.
a. How many non-dimensional groupings can be obtained? Derive them.
b.
If the flow transitions at Re = PV(2R) =2300. Is the generated flow laminar or
turbulent given Q=20 mL/s?
LL
c. Assume the pressure gradient is uniform on the cross-section and can be
calculated using OP=-. The velocity profile in the cylinder is u(r) =
ax
- [1-(²]. Sketch the velocity profile. Calculate the shear stress at the
R² ap
2UÔI
cylinder wall and label the direction.
d.
Calculate the flow rate Q with the velocity profile in (c)..
e. If the shear stress is uniform over the cross-section, i.e. T = C, what's the
pressure gradient distribution and sketch it?
L
L.
R
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