Question

2) Propeller blades in aeroplane are 2m long
(a) When propeller is rotating at 1800 rev/
min, compute the tangential velocity of tip
of the blade.
(b) What is the tangential velocity at a point on
blade midway between tip and axis?
*)
(Ans : 376.8 m/s. 188.4 m/s)

Answer 1

➭ Questíon :-

$⟶$Propeller blades in aeroplane are 2m long

(a) When propeller is rotating at 1800rev/min, compute the tangential velocity of tip of the blade.

(b) What is the tangential velocity at a point on blade midway between tip and axis?

➭ Gíven :-

$⟶$radius,r = 2m

➭ To fínd :-

$⟶$(a) When propeller is rotating at 1800rev/min, compute the tangential velocity of tip of the blade.

$⟶$(b) What is the tangential velocity at a point on blade midway between tip and axis?

➭ Formula requíred :-

$⟶$Angular velocity = Revolution/time

$⟶$Tangential velocity, V = rω

➭ Solutíon :-

(a) Angular velocity, ω = 1800 rev/min

$⟹ w = \frac{180}{60} rev/ s \: \: \: \: \: \: \: \: \: \\ ⟹ w = 30rev/ s \: \: \: \: \: \: \: \: \: \: \: \: \\ ⟹ w = 30 \times 2\pi \: rad / s \\ ⟹ w = 60\pi \: rad / s \: \: \: \: \: \: \: \:$

Tangential velocity, V = rω

$⟹ v = 2 \times 60\pi \: \\ ⟹ v = 120\pi \: \: \: \: \: \: \\ ⟹ v = 377m/s \: \: \:$

(b) Tangential velocity at a point on blade midway between tip and axis:

$⟹ v = \frac{r}{2} \times w \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ⟹ v = 1 \times 60\pi \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ⟹ v = 60\pi \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ ⟹ v = 188.49m/s \: \: \: \: \: \: \: \: \: \:$