Water flows into a large tank with flat bottom at the rate of 10-4 m3 s-1 . Water is also leaking out of a hole of area 1 cm2 at its bottom. If the height of the water in the tank remains steady, then this height (in cm) is:

Question

Water flows into a large tank with flat bottom at the rate of 10-4 m3 s-1 . Water is also leaking out of a hole of area 1 cm2 at its bottom. If the height of the water in the tank remains steady, then this height (in cm) is: (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/a44adfd3e73bd09bad5678a954a85e73-.png" /> Since height of water column is constant therefore, water inflow rate (Q textin) = water outflow rate Q textin = 10-4 m3 s-1 Q textout = Au =10-4 × √2gh ∴ 10-4 =10-4 × √20× h ∴ h=(1/20) m = 5 cm

Q. Water flows into a large tank with flat bottom at the rate of $1 0^{- 4} m^{3} s^{- 1}$ . Water is also leaking out of a hole of area $1 c m^{2}$ at its bottom. If the height of the water in the tank remains steady, then this height (in cm) is:

Since height of water column is constant therefore,
water inflow rate $(Q_{in})$
= water outflow rate
$Q_{in} = 1 0^{- 4} m^{3} s^{- 1}$
$Q_{out} = A u = 1 0^{- 4} \times 2 g h$
$∴ 1 0^{- 4} = 1 0^{- 4} \times 20 \times h$
$∴ h = \frac{1}{20} m = 5 c m$

Q. Water flows into a large tank with flat bottom at the rate of 10−4m3s−1 . Water is also leaking out of a hole of area 1cm2 at its bottom. If the height of the water in the tank remains steady, then this height (in cm) is:

Since height of water column is constant therefore, water inflow rate (Qin​) = water outflow rate Qin​=10−4m3s−1 Qout​=Au=10−4×2gh​ ∴10−4=10−4×20×h​ ∴h=201​m=5cm

Q. Water flows into a large tank with flat bottom at the rate of $1 0^{- 4} m^{3} s^{- 1}$ . Water is also leaking out of a hole of area $1 c m^{2}$ at its bottom. If the height of the water in the tank remains steady, then this height (in cm) is:

Since height of water column is constant therefore,
water inflow rate $(Q_{in})$
= water outflow rate
$Q_{in} = 1 0^{- 4} m^{3} s^{- 1}$
$Q_{out} = A u = 1 0^{- 4} \times 2 g h$
$∴ 1 0^{- 4} = 1 0^{- 4} \times 20 \times h$
$∴ h = \frac{1}{20} m = 5 c m$