a) Explanation Write the expression to calculate the area of pipe. A = π 4 D 2 (I) Here, the diameter of pipe is D . Write the expression for the flow rate using the continuity equation. Q = A V V = Q A (II) Here, the flowrate is Q , area of cross section of pipe is A , and velocity of pipe at point is V . Write the expression for the Reynolds number of the flow. Re = ρ V D μ Re = ( S G ρ w ) V D μ (III) Here, the dynamic viscosity of the water is μ and the density of water is ρ , specific gravity of the fluid is S G , density of water is ρ w . Write the given relationships between the viscosity of water and the asphalt. μ = 80 , 000 μ H 2 O (IV) Here kinematic viscosity of asphalt is μ and kinematic viscosity of water is μ H 2 O . Write the expression for the specific gravity of the corn syrup ( S G ) . S G = γ γ w γ = S G × γ w (V) Here, specific weight of the Asphalt is γ and specific weight of the water is γ w . Write the expression for the Poiseuille law of equation 8.12 for the flow through inclined pipes with laminar flow. Q = π ( Δ p − γ l sin θ ) D 4 128 μ l (VI) Here, pressure drop is Δ p , specific weight is γ , length is l , angle of inclination is θ , diameter of the pipe is D , and dynamic viscosity is μ . Conclusion: Use the Reynolds number to check the flow is laminar or turbulent. Substitute 2 in for D in equation (I). A = π 4 ( 2 in . ) 2 A = π 4 ( 2 in . × 1 ft 12 in . ) 2 = 0 .02182 ft 2 Substitute 4.69 × 10 − 3 ft 3 /s for Q and 0 .02182 ft 2 for A in equation (II). V = 4.69 × 10 − 3 ft 3 /s 0 .02182 ft 2 = 0 .21497 ft/s Substitute 1.09 for S G , 1.94 slug/ft 3 for ρ w , 0 .21497 ft/s for V , 2 in for D , 0.931 lb ⋅ s ft 2 for μ in equation (III). Re = ( 1.09 × 1.94 slug/ft 3 ) ( 0 .21497 ft/s ) ( 2 in . ) 0.931 lb ⋅ s ft 2 Re = ( 1 b) To determine The flow rate of the asphalt when pipe is in vertical

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ISBN: 9781119547990

Author: HOCHSTEIN

Publisher: JOHN WILEY+SONS INC.

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Chapter 8.2, Problem 20P

To determine

The flow rate of the asphalt when pipe is in horizontal.

To determine

The flow rate of the asphalt when pipe is in vertical

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Chapter 8.2, Problem 19P

Chapter 8.2, Problem 21P

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