Question

Look at picture for further clarification. Simplify your answer. Round the final answer to the nearest TENTH as needed. Round all intermediate values to the nearest thousandth as needed.

Answer 1

The formula for the velocity of flow is given by:

`\begin{gathered} v=(r)/(A) \\ \text{where,} \\ r=\text{rate of flow in cps} \\ A=cross\text{ sectional area.} \\ v=\text{ velocity of flow} \end{gathered}`

The cross-sectional area of a pipe is the area of its opening (i.e. the area of a circle). We are told the diameter of the pipe is 2-inches.

Thus, we can calculate the velocity as follows:

`\begin{gathered} r=0.93\text{cfs} \\ we\text{ should convert this into cubic inches for uniformity of units.} \\ 1cubic\text{ foot}\to1728\text{cubic inches} \\ \therefore0.93\text{cubic foot}\to(0.93)/(1)*1728=1607.040\text{ (To the nearest thousandth)} \\ \therefore r=1607.040\text{cubic inches per second} \\ \\ A=\pi((d)/(2))^2=\pi*((2)/(2))^2=\pi\text{ square inches} \\ \\ \therefore v=(1607.040)/(\pi)=511.5367\approx511.537\text{inches per second} \\ \\ \text{But we want the velocity in feet per second. Thus, we say:} \\ 12\text{ inches }\to1\text{foot} \\ \therefore511.537inches\to(511.537)/(12) \\ \\ \therefore v=42.6\text{fps (To the nearest tenth)} \end{gathered}`

The Answer is 42.6fps