Pressure drop across orifice , calculation help

[tweety1234]

Homework Statement

A fluid of relative density 0.86 and viscosity 0.003 pa flows through a pipe of 12cm diameter. The flow rate is measured using an orifice plate with a 6cm diameter orifice, with pressure tapping connected to a differential U-tube manometer using mercury (density = 13600 kg m^{-3} ) as the manometer fluid. The coefficient of discharge of the orifice meter is 0.62. The difference in mercury levels in the manometer is 100mm. Calculate the pressure drop across the orifice plate and the mass flow rate of the fluid. Then calculate the Reynolds number Number based on the orifice diameter.

equations needed ;

$$\bigtriangleup P = (\rho_{F} - \rho) g \bigtriangleup h$$

$$Q = \displaystyle C_{D} A_{0} \sqrt{\frac{2(p_{1}-p_{2})}{\rho (1-\frac{A_{0}}{A_{1}}^{2})}$$

$$Re = \frac{4M}{\pi D \mu}$$

mass flow rate $$Q \rho = m$$

$$A_{0} = 0.01131 m^{2}$$

$$A_{1} = 2.827 m^{2}$$

pressure drop = $$\bigtriangleup P = (\rho_{F} - \rho) g \bigtriangleup h$$

= (13600-860)9.8 x 0.1 = 12485.2 pa

The correct answer is 125000, I think they may have rounded up ?

2) Volumetric flow rate = $$(0.62)(0.01131) \sqrt{\frac{(2\times12485.2)}{13600 ( 1-\frac{0.01131}{2.827}^{2})} = 9.50 \times 10^{-3}$$

mass flow rate = $$(9.50 \times 10^{-3}) \times 860 = 8.17$$the correct answer is $$8.39 kg s^{-1}$$

I can't see where I am going wrong, and help appreciated.

 

[tweety1234]

Anyone know?