The velocity of water flowing through a pipe is inversely proportional to the square of the radius of the pipe. If the velocity of the water is 30cm/s when the radius of the pipe is 2cm. Find the velocity of water when the radius of the pipe is 4cm

Kasi ya maji inapita kwenye bomba inalingana kinyume na mraba wa rediasi ya bomba. Hii inamaanisha:

$$V \propto \frac{1}{r^2}$$

Au kwa kutumia kigezo cha uwiano $k$:

$$V = \frac{k}{r^2}$$

Tunajua kuwa $V = 30 \text{ cm/s}$ wakati $r = 2 \text{ cm}$.

$$30 = \frac{k}{(2)^2}$$ $$30 = \frac{k}{4}$$

Zidisha pande zote mbili kwa 4:

$$k = 30 \times 4$$ $$k = 120$$

Sasa tunataka kupata $V$ wakati $r = 4 \text{ cm}$.

$$V = \frac{120}{(4)^2}$$ $$V = \frac{120}{16}$$

$$V = \frac{120}{16}$$

Gawanya namba zote mbili kwa 8:

$$V = \frac{15}{2}$$ $$V = 7.5 \text{ cm/s}$$

Kasi ya maji wakati rediasi ni $4 \text{ cm}$ ni:

$$7.5 \text{ cm/s}$$