Question

A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 for g.) W = J Enter an exact number. a=4 b = 4 C = 15 d = 4 | Om dm † a m 1 Cm

Answer 1

The work is given by

work = distance x density x volume xg

or, in differential form taking and $\text{density} = 1000$

$\text dW = 9800y \,\text dV$. The total work is given by

$W = \underbrace{\int_0^a 9800 \,y \,\text dV}_{\text{tank}} + \underbrace{9800 \times d \times V}_{\text{pipe }d}$

The differential form is $\text dV =y \times c\times \text dy$ .

Therefore,

$W = \int_0^4 9800 \times y \times y\times 15 \,\text dy + 9800 \times 4 \times 15 \times \frac{4\times 4}2$
$= 147000\int_0^4 y^2 \,\text dy + 4704000$
$= 147000\left[\frac{y^3}3 \right]_0^4 + 4704000$
.