Answer to Question #229934 in Molecular Physics | Thermodynamics for Unknown346307

Question

A 2.2-cm-outer-diameter pipe is to span across a river at a 30-m-wide sec￾tion while being completely immersed in water (). The average

flow velocity of water is 4 m/s and the water temperature is 158C. Determine

the drag force exerted on the pipe by the river.

Answer 1

A pipe is crossing a river. The drag force that acts on the pipe is to be determined.

Assumptions:

1. The outer surface of the pipe is smooth so that Figure can be used to determine the drag coefficient.

2. Water flow in the river is steady.

3. The direction of water flow is normal to the pipe.

4. Turbulence in river flow is not considered.

Properties The density and dynamic viscosity of water at $15 ^{\circ}\; are \;\rho = 999.1 \; kg/m^{3}$ and $\mu = 1.138 \times 10^{-3} \; kg/m$ .

Noting that D = 0.022 m, the Reynolds number for flow over the pipe is

$Re=\frac{VD}{υ}=\frac{ρVD}{\mu} \\ = \frac{(999.1 \;kg/m^3)(4\;m/s)(0.022 \;m)}{1.138 \times 10^{-3} \; kg/m \cdot s} \\ = 7.73 \times 10^4$

The drag coefficient corresponding to this value is, from Figure, $C_{D} = 1.0$ . Also, the frontal area for flow past a cylinder is $A = LD$ . Then the drag force acting on the pipe becomes

$F_D=C_D A \frac{ρV^2}{2} \\ = 1.0 (30 \times 0.022 \;m^2) \frac{(999.1 \;kg/m^3)(4 \;m/s)}{2} (\frac{1\;N}{1 \; kg \cdot m/s^2}) \\ = 5275 \;N$