Question

Calculate the length of water column that can produce the same pressure of column of mercury of (1 mm)length.
please answer me...​

Answer 1

Answer:

Pressure at the place remains the same for both water and mercury.

Pressure exerted by mercury = density of mercury * height of mercury column * g (acc. due to gravity)

=> Pressure exerted by mercury = 13.6*

70*g

=> Pressure exerted by mercury = 952 g.

Pressure exerted by water = density of water * height of water column * g (acc. due to gravity)

=> Pressure exerted by water = 1 * h *g = hg. => Pressure exerted by water =

Now, According to question,

952*g=h* g => h = 952 cm.

Therefore, the height of water column which will exert on its base the same pressure as the 70 cm column of mercury is 952 cm.

Answer 2

The length of the water column that can produce the same pressure as a column of mercury of (1 mm) length is 5.43 mm

Given,

Length of mercury column = 1 mm

To Find,

Length of the water column that exerts the same pressure as that of the mercury column

Solution,

This problem can be solved by using the formula that tells the relationship between pressure (P), the density of the liquid (ρ), the height of the liquid (h), and acceleration due to gravity (g)

P = ρgh

$P_w = \rho_w g_w h_w$

$P_m = \rho_m g_m h_m$

$\frac{P_w}{P_m} = \frac{\rho_w}{\rho_m} \frac{g_w}{g_m} \frac{h_w}{h_m}$

$h_w = \frac{P_w \rho_m g_m h_m}{P_m \rho_w g_w}$

We know gm = gw = g. Also given Pw = Pm = P

$h_w = \frac{\rho_m h_m}{\rho_w}$

Now, density of mercury = 5.43 g/cm cube

density of water = 1 g per cm cube

height of mercury column = 1 mm = 0.1 cm

$h_w = \frac{5.43 \times 0.1}{1}$

$h_w = 0.543 cm$

length of water column = 0.543 cm = 5.43 mm

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