Question

A cylindrical water tank of diameter 1.4 m and 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 m/s in how much time will the be filled​

Answer 1

Answer:

28 min is the answer for your question

Answer 2

Gɪᴠᴇɴ:

$\begin{gathered}\longmapsto\:\:\bf{Diameter\:(d_t)\:=\:1.4\:m} \\ \end{gathered}$

$\begin{gathered}\longmapsto\:\:\bf{Height\:(h_t)\:=\:2.1\:m} \\ \end{gathered}$

Aɴᴅ,

$\begin{gathered}\longmapsto\:\:\bf{Diameter\:(d_p)\:=\:3.5\:cm\:=\:0.035\:m} \\ \end{gathered}$

Water flows through the pipe is 2 m/s.

Tᴏ Fɪɴᴅ :

Time taken to fill the water tank.

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

Wᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ,

↝ Volume of a cylinder is,

$\begin{gathered}\red\bigstar\:\:{\underline{\orange{\boxed{\bf{\green{Volume\:=\:\pi\:r^2\:h\:}}}}}} \\ \end{gathered}$

Cᴀsᴇ - 1 :

★ Here we calculate the volume of the cylindrical water tank.

Wʜᴇʀᴇ,

Radius (rₜ) = $\bf{\dfrac{d_t}{2}\:=\:\dfrac{1.4}{2}}$

Tʜᴜs,

✯ Volume of the water tank is,

$➻ \begin{gathered}\bf{Volume\:=\:\pi\times{(0.7)^2}\times{2.1}\:} \\ \end{gathered}$

$➻ \begin{gathered}\bf{Volume\:=\:\pi\times{0.49}\times{2.1}\:} \\ \end{gathered}$

$➻ \begin{gathered}\bf\blue{Volume_{(tank)}\:=\:1.029\pi\:m^3} \\ \end{gathered}$

Cᴀsᴇ - 2 :

★ Here we calculate the volume of the cylindrical pipe.

Wʜᴇʀᴇ,

Radius (rₚ) = $\bf{\dfrac{d_p}{2}\:=\:\dfrac{0.035}{2}}$

Height (hₚ) = Rate of flow of water = 2 m

$➛ \begin{gathered}\bf{Volume\:=\:\pi\times{(0.0175)^2}\times{2}\:} \\ \end{gathered}$

$➛ \begin{gathered}\bf{Volume\:=\:\pi\times{0.00030625}\times{2}\:} \\ \end{gathered}$

$➛ \begin{gathered}\bf{Volume\:=\:0.0006125\pi\:m^3} \\ \end{gathered}$

$➛ \begin{gathered}\bf\purple{Volume_{(pipe)}\:=\:6.125\pi\:\times{10^{-4}}\:m^3} \\ \end{gathered}$

Nᴏᴡ,

➣ Let us assume that t seconds is required to fill the water tank.

Tʜᴜs,

↝ Volume of the water flows through the pipe in t seconds is,

$\begin{gathered}:\longrightarrow\:\:\bf{6.125\pi\:\times{10^{-4}}\times{t}} \\ \end{gathered}$

✯ We have, volume of the water flows through the pipe in t seconds is equal to the volume of the water tank.

$\begin{gathered}\implies\:\bf{6.125\pi\:\times{10^4}\times{t}\:=\:1.029\pi\:} \\ \end{gathered}$

$\begin{gathered}:\implies\:\bf{t\:=\:\dfrac{1.029\pi}{6.125\pi\:\times{10^{-4}}}\:} \\ \end{gathered}$

$\begin{gathered}:\implies\:\bf{t\:=\:\dfrac{1.029}{6.125}\:\times{10^{4}}\:} \\ \end{gathered}$

$\begin{gathered}:\implies\:\bf{t\:=\:0.168\times{10^4}\:} \\ \end{gathered}$

$\begin{gathered}:\implies\:\bf\pink{t\:=\:1680\:seconds\:=\:28\:minutes} \\ \end{gathered}$

$\Large\bf{Therefore,}$

The time taken to fill the water tank is 1680 seconds or 28 minutes.