Water is conveyed through a uniform tube of 8 cm in diameter and 3140 m in length at the rate 2 × 10-3 m3 per second. The pressure required to maintain the flow is (Viscosity of water = 10-3 )

Question

Water is conveyed through a uniform tube of 8 cm in diameter and 3140 m in length at the rate 2 × 10-3 m3 per second. The pressure required to maintain the flow is (Viscosity of water = 10-3 ) (A)  6.25 × 103 N m-2  (B)  0.625 N m-2  (C)  0.0625 N m-2  (D)  0.00625 N m-2

Tardigrade Admin · Accepted Answer

According to Poiseuille formula,
Rate of flow,

V = \frac{π P r ^{4}}{8 η l}

where the symbols have their usual meanings.

∴ P = \frac{V 8 η l}{π r ^{4}}

Here,

V = 2 \times 1 0^{- 3} m^{3} s^{- 1}

r = \frac{8}{2} c m = 4 c m = 4 \times 1 0^{- 2} m

l = 3140 m, η = 1 0^{- 3} N s m^{- 2}

Substituting the given values, we get

P = \frac{( 2 \times 1 0 ^{- 3} m ^{3} s ^{- 1} ) ( 8 ) ( 1 0 ^{- 3} N s m ^{- 2} ) ( 3140 m )}{( 3.14 ) ( 4 \times 1 0 ^{- 2} m ) ^{4}}

= 6.25 \times 1 0^{3} N m^{- 2}

Q. Water is conveyed through a uniform tube of $8 c m$ in diameter and $3140 m$ in length at the rate $2 \times 1 0^{- 3} m^{3}$ per second. The pressure required to maintain the flow is (Viscosity of water $= 1 0^{- 3}$ )

$6.25 \times 1 0^{3} N m^{- 2}$

$0.625 N m^{- 2}$

$0.0625 N m^{- 2}$

$0.00625 N m^{- 2}$

Q. Water is conveyed through a uniform tube of 8cm in diameter and 3140m in length at the rate 2×10−3m3 per second. The pressure required to maintain the flow is (Viscosity of water =10−3 )

6.25×103Nm−2

0.625Nm−2

0.0625Nm−2

0.00625Nm−2

Q. Water is conveyed through a uniform tube of $8 c m$ in diameter and $3140 m$ in length at the rate $2 \times 1 0^{- 3} m^{3}$ per second. The pressure required to maintain the flow is (Viscosity of water $= 1 0^{- 3}$ )

$6.25 \times 1 0^{3} N m^{- 2}$

$0.625 N m^{- 2}$

$0.0625 N m^{- 2}$

$0.00625 N m^{- 2}$