Flat Plate, Water. Water flows at atmospheric pressure over a flat plate at U = 5m/s. (a) At what distance x* from the leading edge will the flow become turbulent? (b) At x*, assuming laminar flow, what is the (i) boundary layer thickness 8*, (ii) the wall shear stress and (iii) the speed ratios u/U and v/U at y = 8*/2? (c) If a pitot tube, open at the top, is placed at y = 8*/2 and fills with water, what is the pitot manometer height, h (assume Pg = 0 in the boundary layer)? Ans OM: (a) x*: 10-¹ m; (b) 8*: 104 m, Tw: 10¹ Pa, u/U: 10-¹, v/U: 104; (c) h: 10¹ m.
Flat Plate, Water. Water flows at atmospheric pressure over a flat plate at U = 5m/s. (a) At what distance x* from the leading edge will the flow become turbulent? (b) At x*, assuming laminar flow, what is the (i) boundary layer thickness 8*, (ii) the wall shear stress and (iii) the speed ratios u/U and v/U at y = 8*/2? (c) If a pitot tube, open at the top, is placed at y = 8*/2 and fills with water, what is the pitot manometer height, h (assume Pg = 0 in the boundary layer)? Ans OM: (a) x*: 10-¹ m; (b) 8*: 104 m, Tw: 10¹ Pa, u/U: 10-¹, v/U: 104; (c) h: 10¹ m.
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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![**Assumptions:**
- Atmospheric Pressure (Patm) = \(10^5\) Pa
- Atmospheric Pressure in psi (Pa) = 14.7 psi
- Density of Water (pwater) = 1000 kg/m\(^3\)
- Density of Air (pair) = 1.2 kg/m\(^3\)
- Dynamic Viscosity of Water (\(µ_{water}\)) = \(10^{-3}\) Ns/m\(^2\)
- Dynamic Viscosity of Air (\(µ_{air}\)) = \(2 \times 10^{-5}\) Ns/m\(^2\)
- Kinematic Viscosity of Water (\(V_{water}\)) = \(10^{-6}\) m\(^2\)/s
- Kinematic Viscosity of Air (\(V_{air}\)) ≈ \(1.67 \times 10^{-5}\) m\(^2\)/s
- Gravitational Acceleration (g) = 9.8 m/s\(^2\)
- Speed Conversions:
- 1 m/s = 2.24 mph
- 1 lbf = 4.45 N
- 1 m\(^3\) = 264 gallons
Changing variables, the Integral Boundary Layer (IBL) equation 9.21 can be simplified as:
\[ tW = \rho U^2 \left(\frac{dδ}{dx}\right) \left[\int_0^1 \left(\frac{u}{U}\right)(1 - \frac{u}{U})dη\right] \]
Where \( η ≡ \frac{y}{δ} \), with integral limits from 0 to 1. Assuming profiles of the form \( u/U = f(n) \), the integral value is a pure number. For turbulent IBL:
\[ tW = 0.0233 \rho U^2 \left[\nu/(Uδ)\right]^{1/4} \text{ on LHS} \]
---
**Flat Plate, Water:**
Water flows at atmospheric pressure over a flat plate at \( U = 5 \) m/s.
1. **(a)** At what distance \( x^* \) from the leading edge will the flow become turbulent?
- **Answer (OM):** \( x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff46cd712-1d53-471c-8e4d-5e78c3c80932%2F69cb3b01-5f90-4a28-acf3-1595bff576a9%2Fzjquy8_processed.png&w=3840&q=75)
Transcribed Image Text:**Assumptions:**
- Atmospheric Pressure (Patm) = \(10^5\) Pa
- Atmospheric Pressure in psi (Pa) = 14.7 psi
- Density of Water (pwater) = 1000 kg/m\(^3\)
- Density of Air (pair) = 1.2 kg/m\(^3\)
- Dynamic Viscosity of Water (\(µ_{water}\)) = \(10^{-3}\) Ns/m\(^2\)
- Dynamic Viscosity of Air (\(µ_{air}\)) = \(2 \times 10^{-5}\) Ns/m\(^2\)
- Kinematic Viscosity of Water (\(V_{water}\)) = \(10^{-6}\) m\(^2\)/s
- Kinematic Viscosity of Air (\(V_{air}\)) ≈ \(1.67 \times 10^{-5}\) m\(^2\)/s
- Gravitational Acceleration (g) = 9.8 m/s\(^2\)
- Speed Conversions:
- 1 m/s = 2.24 mph
- 1 lbf = 4.45 N
- 1 m\(^3\) = 264 gallons
Changing variables, the Integral Boundary Layer (IBL) equation 9.21 can be simplified as:
\[ tW = \rho U^2 \left(\frac{dδ}{dx}\right) \left[\int_0^1 \left(\frac{u}{U}\right)(1 - \frac{u}{U})dη\right] \]
Where \( η ≡ \frac{y}{δ} \), with integral limits from 0 to 1. Assuming profiles of the form \( u/U = f(n) \), the integral value is a pure number. For turbulent IBL:
\[ tW = 0.0233 \rho U^2 \left[\nu/(Uδ)\right]^{1/4} \text{ on LHS} \]
---
**Flat Plate, Water:**
Water flows at atmospheric pressure over a flat plate at \( U = 5 \) m/s.
1. **(a)** At what distance \( x^* \) from the leading edge will the flow become turbulent?
- **Answer (OM):** \( x
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