ME 3111 ch6
The viscous flow regimes (laminar, transitional, and turbulent) in ducts are primarily based on the value of _____.
Reynolds number
Calculate the sublayer thickness ys (in terms of d) if the Reynolds number is 105 and Darcy friction factor f = 0.0180.
0.001d
True or false: Losses due to gradual expansions or contractions are called the major losses in pipe systems.
False
True or false: The gate valve produces maximum loses when fully open among all the other valves.
False
True or false: If a duct is noncircular, the analysis of fully developed flow follows that of the circular pipe but is more complicated algebraically.
True
True or false: For elbows in a pipe, the loss factors are highly dependent on actual design and manufacturing factors.
True
If the entrance is from a finite reservoir between two sizes of pipe, it is termed as a sudden _____.
contraction
The loss coefficient formula for sudden contraction, K ≈ 0.42(1−d2D2), is valid up to the value _____.
d/D = 0.76
The loss coefficient formula for sudden contraction, K ≈ 0.42(1−d^2/D^2)1, is valid up to the value _____.
d/D = 0.76
For internal flows through pipe networks, the net flow into any junction must be ____ .
0
Match the ε/d values (in left column) with their respective friction factor values (in right column) for a fully rough flow.
0.00001 matches Choice, 0.00806 0.0001 matches Choice, 0.0120 0.01 matches Choice, 0.0379 0.05 matches Choice, 0.0716
Identify the Prandtl equation for turbulent flow in smooth pipes.
1/(f^1/2) = 2.0 log (Redf^1/2) - 0.8
Identify the equation for fully rough flow in ducts.
1/f1/2 = -2.0 log (ε/d)/3.7
Identify the Colebrook equation that combines the smooth wall and fully rough flow relations
1/f1/2 = -2.0 log((ε/d)/3.7+(2.51)/Redf1/2)
Identify the friction factor equation for turbulent flow between two parallel plates.
1/f1/2 = 2.0 log (0.64ReDhf1/2)0.64ReDhf1/2 - 0.8
Identify the Prandtl equation for turbulent flow in smooth pipes
1/f1/2 = 2.0 log (Redf1/2) - 0.8
Transition from laminar to turbulence occurs when the Reynolds number is in the range _____.
10^3 < Re < 10^4
The maximum possible laminar entrance length, at Red,crit = 2300, is Le = _____
138d
The maximum possible laminar entrance length, at Red,crit = 2300, is Le = _____.
138d
In a noncircular duct, the laminar solution becomes unstable and transition from laminar to turbulent occurs at ReDh ≈ _____.
2000
Calculate the hydraulic diameter of a noncircular duct if its wetted perimeter is 32 cm and area is 25 cm^2
3.125 cm
Blasius equation for turbulent flow f = 0.316 Red−1/4Red-1/4holds good only when the Reynolds number is in the range __
4000 < Re < 10^5
Calculate the effective diameter of a non circular duct if the hydraulic diameter is 100 cm. Assume the flow to be turbulent.
64 cm
Identify true statements about a gradually expanding diffuser.
A thinner entrance boundary layer causes a slightly smaller loss than a fully developed inlet flow. Head loss can be large if the cone angle is too great.
Identify the true statements about the losses in pipe entrance and exit.
At a submerged exit, the flow goes out of the pipe into the reservoir and loses all its velocity head. Sharpe edges or protrusions at the entrance cause large zones of flow separation and large losses.
Identify the loss coefficient (K) formula for losses in sudden expansion internal flows.
K = (1−d^2/D^2)^2
For a flow through the pipe, identify the steps for determining the friction factor using the Moody chart if the velocity (V), diameter (d), roughness (ε), and viscosity (υ) are given.
Calculate the Reynolds number. Calculate the relative roughness of the pipe. Use the Reynolds number and relative roughness values to determine the friction factor value from Moody chart
Identify the parameters that are equal to the head loss in a pipe for a fully developed flow.
Change in sum of pressure and gravity head Change in height of the hydraulic grade line
Identify the types of problems which are mainly encountered in pipe flow calculations.
Computing the pipe length where Q, d, hf, ρ, μ, and g are given and the pipe length L is computed. Head loss problem where d, L, and V or Q, ρ, μ, and g are given and head loss is computed. Sizing problem where ρ, Q, L, hf, μ, and g are given and the diameter d of the pipe is computed.
For all submerged exits, the value of the loss coefficient is _____.
K = 1
In the Prandtl equation for turbulent flow in smooth pipes 1f1/21f1/2 = 2.0 log (Redf1/2)Redf1/2 - 0.8, f is called the _____.
Darcy friction factor
Identify the equation for effective diameter which is used in the turbulent flow equation for obtaining a more accurate turbulent friction solution.
Deff = Dh(64)/(fReDh)laminar theory
The hydraulic diameter value used in the laminar and turbulent equations for flow through concentric annulus is _____.
Dh = 2(a - b)
Identify the reasons for a larger loss due to a bend or curve in a pipe than a straight pipe.
Due to the swirling secondary flow arising from centripetal acceleration Due to the flow separation on curved walls
For an elbow, the equation for determining the resistance coefficient is _____.
K = hm/(V^2/2g)
Identify the curve-fit formula for the 90° bend in turbulent flow.
K ≈ 0.388α(R/d)^0.84 ReD^-0.17
Identify the loss coefficient (K) formula for losses in sudden contraction internal flows.
K ≈ 0.42(1−d2/D2)
Identify the true statements about the internal flow through pipes in series.
For pipes in series, the total head loss through the system equals the sum of head loss in each pipe. The flow rate is same in all the pipes that are in se
Identify the loss coefficient formula for a gradually expanding diffuser.
K ≈ 2.61 sinθ(1−d2/D2)^2 + favg(L/davg)
Which of the following valve when opened fully has the highest loss?
Globe valve
Identify the dimension of the Darcy friction factor.
It is a dimensionless parameter
Identify the true statements about flow analysis in noncircular ducts.
Laminar flow problems for noncircular ducts can be solved by computing the exact equation of continuity and momentum. Turbulent flow problems for noncircular ducts can be solved using the logarithm law velocity profile or the hydraulic diameter approximation
Identify the minor or local losses in pipe systems.
Losses due to pipe entrance or exit. Losses due to sudden expansion or contraction. Losses due to elbows.
Identify the true statements about the four main pipe flow problems
Multiple iterations and repeated calculations are carried out to compute the velocity V. The head loss problem can be solved directly by referring to the Moody chart.
If the _____ values are available, then the friction factor can be determined using the Moody chart.
Reynolds number and relative roughness
In laminar flow, the pipe friction factor (Darcy friction factor) decreases inversely with _____ number
Reynolds
In an internal flow, the only parameter that affects the entrance length is _____.
Reynolds number
The accepted critical value of Reynolds number for pipe flow transition is ____
Red,crit ≈ 2300
The accepted critical value of Reynolds number for pipe flow transition is _____.
Red,crit ≈ 2300
Identify the true statements about the the effect of rough walls.
Surface roughness has an effect on friction resistance. Turbulent flow is strongly affected by roughness.
In pipes, critical flow occurs at a Reynolds number Re ≈2300. What can be inferred from this statement?
The flow changes from laminar to turbulent.
Identify the basic rules which are used for solving the pipe network problems.
The net flow into any junction must be zero. All pressure changes must satisfy the Moody and minor-loss friction correlations.
Identify the true statements about the losses in bends of a pipe system.
The secondary and separation flow losses decrease with the R/d ratio. Due to the presence of bends in pipe, swirling secondary flow arises that causes losses in pipe system.
The accepted transition Reynolds number for flow in a circular pipe is Re ≈ 2300. For flow through a 10-cm-diameter pipe, at what velocity will the transition occur at 20°C for airflow. The density and viscosity of air at 20°C are 1.205 Kg/m3 and 1.80 E-5 kg/(m⋅s).
Velocity is calculated using the formula for Reynolds number Re = ρVd/μ. Substituting the given values, V = 0.34 m/s.
Identify the true statements about the viscous flow regimes (laminar, transitional, and turbulent) in ducts.
When the Reynolds number is in the range of 1 < Re < 100, the flow is laminar and it depends strongly on Reynolds number. When the Reynolds number is in the range of 106 < Re < ∞, the flow is turbulent and there is a slight Reynolds number dependence.
The losses due to sudden ____ in a pipe is because the exit is to a finite-sized pipe.
expansion
Identify the Blasius equation for turbulent flow in smooth pipes if Re is the Reynolds number, f is the Darcy friction factor, e roughness of the pipe, and D diameter of the pipe.
f = 0.316 Red^−1/4
Identify the formula used for determining the Darcy friction factor in laminar pipe flows.
f = 64/Red
Identify the friction factor equation for laminar flow through concentric annulus.
f = 64ζ/ReDh
Identify an equation that defines friction factor in terms of average shear stress
fNCD = 8τw/ρV^2
Identify the head loss equation for a fully developed laminar flow in pipes.
hf = (128μLQ)/(πρgd^4)
Identify the equation to determine the head loss due to friction for laminar internal flow between two parallel plates.
hf = 3μLV/ρgh^2
Identify an equation that relates the head loss in a pipe to the wall shear stress
hf = 4τwL/ρgd
Identify an equation that relates the head loss in a pipe to the wall shear stress.
hf = 4τwL/ρgd
Identify the head loss relation for internal flows through pipes in parallel.
hf = Q^2/(ΣCi/fi√)2
For pipes in parallel, each pipe is related to the head loss (hf) by the Moody relation _____.
hf = f(L/D)(V2/2g)
If Dh is the hydraulic diameter, d is the diameter of the pipe, L is the length, f is the friction factor, and V is the velocity, identify the head loss equation for turbulent flow in a noncircular duct.
hf = f(L/Dh)(V^2/2g)
Identify the correct relationship between head loss and the Darcy friction factor for a pipe flow
hf = f(L/d)(V^2/2g)
Identify an equation to calculate the pipe length from Darcy's formula.
hf = f(LV^2)/2dg
For turbulent flow in a noncircular duct, the ratio of four times the area to that of the wetted perimeter is known as the
hydraulic diameter
The losses that occur due to tees, elbows, and other fittings is called ____ losses.
minor or local
In the derivation for head loss equation for laminar flow in ducts, the quantity Δp is the pressure drop in a pipe of length L and thus the term (dp/dx) is _____
negative
For turbulent flow in a noncircular duct, the accuracy of using Moody chart is _____.
±15%
The accuracy of using the Moody chart for laminar flow in a noncircular duct is
±40%
The accuracy of using the Moody chart for laminar flow in a noncircular duct is _____.
±40%
Consider three pipes A, B, and C are in series and f is the friction factor and α is the dimensionless constant for each pipe. Identify the head loss equation which is used for analyzing internal flow through these pipes.
ΔhA→B = V212gV122g(α0 +α1f1 +α2f2 + α3f3)
Identify the equation of head loss for internal flows through one of the branches of a three-reservoir junction.
Δhi = V^2i/2g fiLi/di
If the pipe has constant diameter, the equation for total system loss is calculated using the formula _____.
Δhtot = V^2/2g((fL)/d+ΣK)
Identify the equations that represent pressure drop in horizontal pipes for low turbulent Reynolds numbers.
Δp ≈ 0.158Lρ3/4μ1/4d-1.25V7/4 Δp ≈ 0.241Lρ3/4μ1/4d-4.75Q7/4
For the contractions and expansions, laminar minor loss coefficient (Klam) is based upon the _____ in the smaller section of the pipe.
velocity
For an incompressible, one-dimensional, steady flow through a horizontal pipe with constant cross section, identify the conditions that are applied to the energy equation for determining the head loss.
z1 = z2 V1 = V2 = V Q1 = Q2 = constant
Identify the roughness height relation used for determining the effect of rough walls on a fluid flow.
ε+ = εu*/ν