Question

7. A large container, 114 cm deep is filled with water. If a small hole is punched in its side 95.0 cm from the top, at what initial speed will the water flow from the hole?

Answer 1

The initial speed of 1.93m/s.

The initial speed of water flowing out of a hole in a container can be calculated using Torricelli's Law, which is derived from Bernoulli's Principle and the conservation of energy. The formula for the initial velocity
`(\( v \))` of the efflux is:

`\[ v = √(2gh) \]`

where:

-
`\( g \)` is the acceleration due to gravity
`(\( 9.81 \, \text{m/s}^2 \)` on Earth),

-
`\( h \)` is the height of the water column above the hole in meters.

In this case, the container is 114 cm deep and the hole is 95.0 cm from the top, which means the height
`\( h \)` of the water column above the hole is:

`\[ h = 114 \, \text{cm} - 95.0 \, \text{cm} = 19.0 \, \text{cm} = 0.19 \, \text{m} \]`

Now we can calculate the initial velocity of the water flowing out:

`\[ v = \sqrt{2 * 9.81 \, \text{m/s}^2 * 0.19 \, \text{m}} \]`

Let's do the calculation.

The initial speed at which the water will flow from the hole is approximately
`\( 1.93 \, \text{m/s} \)`. Here's how we got the result:

1. We first converted the height of the water column above the hole into meters:
`\( 19.0 \, \text{cm} \) is \( 0.19 \, \text{m} \).`

2. Then we applied Torricelli's Law using the formula
`\( v = √(2gh) \)`, with
`\( g \)` being the acceleration due to gravity
`(\( 9.81 \, \text{m/s}^2 \)) and \( h \)`the height of the water above the hole.

3. The calculation yields
`\( v = √(2 * 9.81 * 0.19) \), which gives us the initial speed of \( 1.93 \, \text{m/s} \).`

Answer 2

The initial speed of the water from the hole is determined as 1.93 m/s.

How to calculate the initial speed of the water?

The initial speed of the water is calculated by applying the following formula as shown below;

K.E = P.E

¹/₂mv² = mgh

v² = 2gh

v = √ (2gh)

where;

• h is the height of fall of the water
• g is acceleration due to gravity
• v is the initial speed of the water from the hole

The vertical distance of water from the initial position to the point where the hole is made is calculated as;

h = 114 cm - 95 cm

h = 19 cm

h = 0.19 m

The initial speed of the water is calculated as;

v = √ ( 2 x 9.8 x 0.19 )

v = 1.93 m/s