Consider incompressible flow in a circular channel. Derive general expressions for Reynolds number in terms of (a) volume flow rate and tube diameter and (b) mass flow rate and tube diameter. The Reynolds number is 1800 in a section where the tube diameter is 10 mm. Find the Reynolds number for the same flow rate in a section where the tube diameter is 6 mm.
Consider incompressible flow in a circular channel. Derive general expressions for Reynolds number in terms of (a) volume flow rate and tube diameter and (b) mass flow rate and tube diameter. The Reynolds number is 1800 in a section where the tube diameter is 10 mm. Find the Reynolds number for the same flow rate in a section where the tube diameter is 6 mm.
Consider incompressible flow in a circular channel. Derive general expressions for Reynolds number in terms of (a) volume flow rate and tube diameter and (b) mass flow rate and tube diameter. The Reynolds number is 1800 in a section where the tube diameter is 10 mm. Find the Reynolds number for the same flow rate in a section where the tube diameter is 6 mm.
a)
Expert Solution
To determine
The general expression for Reynolds number in terms of volume flow rate and tube diameter.
Explanation of Solution
Given:
Tube diameter 1(D1) is 10mm.
Tube diameter 2(D2) is 6mm.
Reynolds number 1(Re1) is 1800.
Calculation:
Write the equation for the volume flow rate (Q).
Q=AV¯
Write the equation for the mass flow rate (m˙).
m˙=ρAV¯
Write the equation for the cross sectional area (A).
A=πD24
Calculate the Reynolds number in terms of volume flow rate and tube diameter (Re).
Re=ρDV¯μ=ρDμ(QA)=ρDμ(QπD24)=4QπDρμ
=4QπD(1V¯)=4QπDV¯
Thus, the Reynolds number in terms of volume flow rate and tube diameter is 4QπDV¯.
b)
Expert Solution
To determine
The general expression for Reynolds number in terms of mass flow rate and tube diameter and the Reynolds number for the same flow rate in the section.
Explanation of Solution
Calculate the Reynolds number in terms of mass flow rate and tube diameter (Re).
Re=ρDV¯μ=Dμ(ρV¯AA)=Dμ(m˙πD24)=4m˙πDμ
Thus, the Reynolds number in terms of mass flow rate and tube diameter is 4m˙πDμ.
Calculate the Reynolds number for the same flow rate in the section (Re2).
D1Re1=D2Re2
Re2=D1D2Re1=(10mm)(6mm)(1800)=3000
Thus, the Reynolds number for the same flow rate in the section is 3000.
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4. The flow rate of water through a commercial steel pipe with a diameter of 10
cm and roughness of 0.045 mm is 0.04 m³/s. Try to calculate the difference
height H in water level between the two pools. The valve and the bend loss
coefficients are 5.7 and 0.64, respectively. The inlet and outlet loss coeffi-
cients are 0.5 and 1.0, respectively. Kinematic viscosity of water is 1-10-6
m²/s. Round off your answer to one decimal digit in m, but enter the answer
without the unit.
Water
20°C
Valve
20m
Bend
10m
20m
commercial steel pipe
diameter of 10cm
Figure 1: Problem 4.
H
6 m
6 m
Elbow
6 m
3 m
1
15 m
A fluid is pumped at a rate of 0.00156
m3/s through a 0.025-m-diameter
pipe to fill a water tank as shown in
Figure. What is the pressure drop
between the inlet (section 1) and the
outlet (section 2) accounting for all
losses?
The density of the fluid is (1.05x10^3)
kg/m3 and the dynamic viscosity
is 1.12 x 10 - 3 Ns/m². The following
are also known KL. elbow = 1.5, KĻ, exit
= 1 and surface roughness, ɛ = 0.001
%3D
mm. Also take gravity, g = 10 m/s².
%3D
A centrifugal pump is used to supply a highly viscous fluid to a chemical plant. The chemicalplant is located at a height of 20 m from the pumping station level. The flow rate required tobe pumped is 0.005 m3
/s. The pipe diameter used for pumping is 30 cm and the total length ofthe pipeline is 50 m. The pipe exits to atmospheric conditions. Compute the Reynolds numberand determine whether the flow is laminar or turbulent. Determine the pressure that should bedelivered by the pump at its exit in order to maintain the flow. Also compute the power inputfor the pump assuming a pump efficiency of 100 %. Take the viscosity of the fluid to be0.01Pa.s. Take the density of the fluid to be 1500 Kg/m3
.
Chapter 8 Solutions
Fox And Mcdonald's Introduction To Fluid Mechanics
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